s 


CD 


LIBRARY 

OF  Till. 


UNIVERSITY  OF  CALIFORNIA. 


Received 


./  ,AV 


,  1890  . 


/ 


Accession  No.  (Q  JJ'eZ  3      •    Class  No. 


0 


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3J£^ 

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ECLECTIC  EDUCATIONAL  SERIES. 


RAY'S 


NEW  INTELLECTUAL 


ARITHMETIC 


VAN   ANTWEEP,    BEAGG    &    CO. 


137  WALNUT  STREET, 
CINCINNATI. 


28  BOND  STREET, 
NEW  YORK. 


.-. 

RAY'S  MATHEMATICAL  SERIES. 


REGULAR   SERIES. 

Ray's  New  Primary  Arithmetic. 
Ray1  s  New  Intellectual  Arithmetic. 
Ray's  New  Practical  Arithmetic. 
Ray's  New  Higher  Arithmetic. 
Ray's  New  Test  Examples. 
Ray's  New  Elementary  Algebra. 
Ray's  New   Higher  Algebra. 
Ray's   Test  Problems  in  Algebra. 
Ray's  Plane  and  Solid  Geometry. 
Ray's   Geometry  and   Trigonometry. 
Ray's  Analytic   Geometry. 
Ray's  Elements  of  Astronomy. 
Ray's  Surveying  and  Navigation. 
Ray's  Differential  and  Integral  Calculus. 

TWO-BOOK   SERIES   IN   ARITHMETIC. 

Ray 's  New  Elementary  Arithmetic. 
Ray's  New  Practical  Arithmetic. 


COPYRIGHT, 

1877, 
BY  VAN  ANTWERP,  BRAGG  &  Co. 


^clectic  £ress: 

VAN   ANTWERP,   BRAGG  &  CO.,   CINCINNATI, 


PEEFACE. 


FKW  works  on  Intellectual  Arithmetic  have  received  more  un- 
qualified approbation,  and  a  more  extensive  patronage,  than  this, 
which,  for  several  years,  was  published  under  the  title — Ray's  Arith- 
metic, Part  Second. 

The  numerous  editions  demanded  have  again  rendered  necessary 
a  renewal  of  the  plates;  this  has  afforded  an  opportunity  for  re- 
modeling the  work. 

Many  important  improvements  have  been  introduced,  with  a 
design  to  impart  completeness,  and  give  a  concise  and  progressive 
course  of  arithmetical  analysis. 

The  volume  in  its  present  form,  embraces: 

1st.  Exercises  on  the  primary  principles,  and  their  applications; 
together  with  models  of  analysis  in  the  shape  of  solutions. 

2d.  A  progressive  and  comprehensive  presentation  of  Fractions, 
intended  to  render  the  subject  intelligible  and  attractive. 

3d.  General  Reviews,  designed  to  test  the  pupil's  knowledge  of 
principles,  preparatory  to  the  applications  of  mental  analysis  which 
follow. 

4th.  Reduction  and  Percentage,  with  the  application  of  the  latter 
to  Profit  and  Loss,  Commission,  Insurance,  Interest,  and  Discount. 

The  value  of  Intellectual  Arithmetic  is  so  highly  appreciated, 
that  little  need  be  said  in  its  commendation;  when  properly  taught, 
it  is  one  of  the  most  useful  and  interesting  studies  in  which  pupils 
can  engage.  By  its  study,  the  pupil  is  taught  to  reason,  to  analyze, 
to  think  for  himself;  while  it  imparts  confidence  in  his  reasoning 
powers,  and  strengthens  the  mental  faculties. 

CINCINNATI,  May,  1877. 


TO  TEACHEES. 


THE  solution  of  an  example  in  Mental  Arithmetic  is  herein  re- 
garded as  a  direct  and  natural  response  to  the  requirements  of  the 
problem;  it  aims  to  be  a  plain  and  simple  statement  of  the  successive 
steps  leading  to  the  final  result  or  answer.  The  data  aiforded  by  the 
example  are  repeated  in  the  solution  no  further  than  is  necessary  for 
its  clear  statement. 

Every  different  class  of  examples  is  furnished  with  a  solution; 
in  a  few  instances,  more  than  one  solution  is  given,  the  succeeding 
solutions  offering  a  briefer  method.  No  solution  is  repeated;  and, 
when  a  solution,  in  whole  or  in  part,  occurs  in  a  subsequent 
solution  as  a  portion  of  the  argument,  its  result  is  given  as  briefly 
as  possible. 

Of  course,  there  is  nothing  to  prevent  the  teacher  from  elabo- 
rating any  solution,  or  any  portion  of  it,  to  the  fullest  extent  he  sees 
fit;  and  it  may  often  be  desirable  so  to  do.  Furthermore,  those 
who  wish  can,  with  facility,  apply  the  "  Four  Step  Method "  for 
the  three  step,  of  which  each  solution  will  furnish  a  clear  state- 
ment. 

It  is  obvious,  that  in  a  text-book  the  publishers  should  not 
occupy  space  with  any  thing  more  than  the  essentials  of  a  solu- 
tion. 


NOTE. — Pupils  who  have  studied  Eay's  New  Primary  Arithmetic, 
ir.ay  commence  with  Lesson  IV,  page  11. 

Numeration  is  the  art  of  reading  numbers. 

Learn '.the  names  arid  forms  of  these  figures: 

1,        2,         3,         4,        5,      '6,        7,          8,         9,      10. 
One,     two,     three,      four,      five,     six,     seven,      eight,     nine,     ten. 


J. 


(5) 


LESSON  I. 

1.  James   had   1    apple,  and   his   brother  gave   him   1 
more:   how  many  had  ho  then?    Ans.  2. 

Why?    Ans.  Because  1  and  1  are  2. 

2.  Henry  had  2  cents,  and  his  sister  gave  him  1  cent 
more :  how  many  had  he  in  all  ?    Ans.  3. 

Why?    Ans.  Because  2  and  1  are  3? 

3.  A  boy  had   1  marble,  and  found  3  marbles  more: 
how  many  did  he  then  have?    Ans.  4. 

Why?    Ans.  Because  1  and  3  are  4. 

4.  Thomas   had   4  cents,  and    his  mother  gave  him   1 
cent  more :   how  much  had  Thomas  altogether  ? 

5.  Samuel   had   2   cakes,  and   his   father  gave   him   2 
more:    how  many  did  he  then  have? 

6.  How  many  are  3  oranges  and  2  oranges? 

7.  James   had   3   apples,  and   his  brother  gave   him  3 
more :   how  many  apples  had  James  then  ? 

8.  John  had  4  plums,  and  his  sister  gave  him  2  more : 
how  many  did  he  then  have? 

9.  Daniel  had  3  cents ;   his  brother  gave  him  2  cents, 
and  his  sister  1  cent:   how  many  did  he  then  have? 

10.  Mary  had    4   pears,  and   her  brother  gave   her  3 
more:   how  many  did  she  then  have? 

11.  How  many  fingers  have  you  on  one  hand?    How 
many  on  both  hands? 

12.  Ida  had  4  cents ;  her  mother  gave  her  3  cents  more 
at  one  time,  and  1  cent  at  another :  how  many  cents  had 
she  altogether? 

(6) 


ADDITION.  7 

13.  Three   cakes   and   3    cakes   and    2   cakes   are   how 
many  cakes? 

14.  Four  cents  and  3  cents  and  2  cents  are  how  many 
cents  ? 

15.  Five  oranges  and  2  oranges  and  1  orange  are  how^ 
many  oranges? 

16.  Henry  had   5    cents,  and   his   mother  gave   him   2 
more  at  one  time,  and  3  at  another:    how  many  did  he 
then  have? 

17.  Five  boys  and   4  boys  and  1  boy  are  how  many 
boys? 

18.  Oliver  has  5  dollars;  Henry,  3  dollars;  and  Samuel, 
1  dollar:  how  many  dollars  have  all  together? 

19.  Three  peaches  and  6  peaches  and  1  peach  are  how 
many  peaches? 

20.  A  lady  paid  1  dollar  for  gloves,  3  dollars  for  a  shawl, 
and  3  dollars  for  a  dress:  how  much  did  she  spend? 

21.  Four  cents  and  3  cents  and  3  cents  and  1  cent  are 
how  many  cents? 

22.  If  a   man   buy  6   pounds  of  sugar  at  one  time,  2 
at  another,  and   2  at  another,  how  much  does   he  buy? 

23.  Seven  oranges  and  1  orange  and  2  oranges  are  how 
many? 

24.  George    has    3    cents,   his    sister    2    cents,   and    his 
brother  2  cents:   if  all  the  money  were  given  to  George, 
how  much  would  he  have? 

25.  How  many  are  4  and  4  and  2? 

26.  James   has   4   cents,  Joseph   2,  and   John    2:    how 
many  cents  have  they  all? 

Addition  is  the  process  of  uniting  two  or  more  num- 
bers. The  result  is  called  the  swwi,  or  amount. 

The  sign  of  addition  (-f )  is  called  plus.  The  sign  of 
equality  (=)  is  read  equals,  or  is  equal  to. 


BAY'S    NEW   INTELLECTUAL  ARITHMETIC. 


LESSON  II. 

1.  One  and  1   are  how  many  ?      1  and  2  ?      3  and  1  ? 
4  and  1 ?      1  and  3  ?      1  and  5  ?      1  and  6  ?      6  and  1  ? 

1  and  7  ?     8  and  1 ?     9  and  1 ?      1  and  8  ? 

i 

SOLUTION. — One  and  one  are  two. 

2.  Two  and  4  and  1  are  how  many?     6  and  2  and  3? 

4  and  1  and  4? 

SOLUTION. — Two  and  four  are  six;  six  and  one  are  seven. 

3.  Five  and   2  are   how  many?    7  and   3?    2   and   6 
and  1?     2  and  1  and  2?     3  and  5?     5  and  4? 

4.  Nine  and  2  are  how  many?     6  and  1  and  1  ?     6  and 
3?     6  and  4?    7  and  1  and  3?     1  and  2  and  8?     1  and 
3  and  8? 

5.  Eight  and  2  are  how  many?     8  and  3?     10  and  2 
and  1?     1  and  4  arid  6?     8  and  4?     7  and  4?     6  and  7? 
7  and  1  and  4?     1  and  8  and  2  and  2? 

6.  Ten  and   2  are  how  many?      9   and   3?      9  and   1 
and  2?      9  and   1  and  3?      5  and  6?      1  and  4  and  8? 

2  and   4   and   6?      3   and   4   and   5?      4   and   7  and   2? 

5  and  4  and  8? 

7.  How  many  are  1   and    9?      10  and   3?     4  and  9? 
7  and  1?     5  and  7?     9  and  4?     2  and  12?     3  and   11? 
Give  two  numbers  which,  added  together,  make  10? 

8.  Begin  at  4,  and  add  2  each  time  up  to  16. 

9.  Begin  at  1,  and  add  3  each  time  up  to  13. 

10.  Mention  two  numbers  which,  added  together,  will 
make  12?     Three  numbers? 

11.  Seven  and  5  and  2  are  how  many? 

12.  Seven  and  3  and  4  are  how  many? 


ADDITION.  9 

13.  If  3  bo  added  to  3,  and  that  sum  to  5,  what  will 
be  the  result? 

14.  If  you  add  3  to  the  sum  of  3  and  1,  and  then  add 

7  more,  what  will  be  the  amount? 

15.  I  have  in  one  basket  8  dozen  eggs,  in  another  4 
dozen,  in  another  3  dozen  :    how  many  eggs  in  all  ? 

SOLUTION. — I  have  in  all  8  dozen  and  4  dozen  and  3  dozen  eggs. 

8  dozen  and  4  dozen  are  12  dozen;    12  dozen  and   3  dozen  are  15 
dozen. 

16.  A  little  girl  bought  two  yards  of  tape  for  3  cents, 
some  pins  for  5  cents,  and  received  2  cents  in  change : 
how  many  cents  had  she  at  first? 

17.  Two  and  1  more,  and  3  and  4  more,  are  together 
how  many? 

18.  One  and   3  and  4  and   5  are  how  many?     5  and 
1  and  3:  and  4? 

19.  A  boy  bought    3   cents  worth   of  marbles,   and    2 
cents  worth  of  candy,  and  received  5  cents  in   change : 
how  much  money  had  he? 

20.  I  bought  three  hams  for  8  dollars,  and  ten  bushels 
of  apples  for  3  dollars:   how  much  did  I  spend? 

21.  Oliver  has  4   cents   in    one    hand,  3   in    the  other, 
and  4  in  his  pocket:  how  many  cents  has  he? 

22.  A  lady  made  two  coats  from  8  yards  of  cloth,  two 
vests  from  2  yards,  and  two  pairs  of  pants  from  6  yards : 
how  many  yards  of  cloth  did  she  use  in  all  ? 

23.  A  grocer  sold  a  pound  of  rice  for  5  cents,  a  paper 
of  matches  for  3  cents,  and  a  box  of  mustard  for  10  cents : 
how  much  did  he  receive  for  all  ? 

24.  How  many  are  9   and  3  and  2  ?     4  and  6  and  8  ? 
10  and  7  and  3? 

25.  If  I  have  10  cents  in  one  pocket,  5  cents  in  another, 
and  3  cente  in  each  hand,  how  much  have  I  altogether? 


10        KAY'S    NEW   INTELLECTUAL  ARITHMETIC. 


LESSON  III. 


ADDITION  TABLE. 


2  +    1=    3 

3+    1=   4 

4+    1=    5 

2  +    2=   4 

3+    2=    5 

4+    2=    6 

2+    3=    5 

3+    3=    6 

4+    3=    7 

2+    4  =    6 

3+    4=    7 

4+    4=    8 

2+    5=   7 

3+    5=    8 

4+    5=    9 

2+    6  =    8 

3+    6=    9 

4+    6  =  10 

2+    7=    9 

3+    7  =  10 

4+    7  =  11 

2  +    8  =  10 

3+    8  =  11 

4+    8  =  12 

2+    9  =  11 

3+    9  =  12 

4+    9  =  13 

2  +  10  =  12 

3  +  10  =  13 

4  +  10  =  14 

2  +  11  =  13 

3  +  11  =  14 

4  +  11  =  15 

2  +  12  =  14 

3  +  12  =  15 

4+12  =  16 

5+    1=    6 

6+    1=   7 

7+1=8 

5+    2=   7 

6+    2=    8 

7+    2=    9 

5+    3=    8 

6+    3=    9 

7+    3  =  10 

5+    4=    9 

6+    4  =  10 

7+    4  =  11 

5+    5  =  10 

6+    5  =  11 

7+    5  =  12 

5+    6  =  11 

6+    6  =  12 

7+    6  =  13 

5+    7  =  12 

6+    7  =  13 

7+    7  =  14 

5+    8  =  13 

6+    8  =  14 

74.    8  =  15 

5+    9  =  14 

6+    9  =  15 

7+    9  =  16 

5  +  10  =  15 

6  +  10  =  16 

7  +  10  =  17 

5  +  11  =  16 

6  +  11  =  17 

7  +  11  =  18 

5  +  12  =  17 

6  +  12  =  18 

7  +  12  =  19 

ADDITION. 


11 


8+    1=    9 

9+    1  =  10 

10+    1  =  11 

8+    2  =  10 

9  +    2  =  11 

10+    2  =  12 

8+    3  =  1] 

9+    3  =  12 

10+    3  =  13 

8+    4=12 

9+    4  =  13 

10+    4  =  14 

8+    5  =  13 

9+    5  =  14 

10+    5  =  15 

8-f    6  =  14 

9+    6  =  15 

10+    6  =  16 

8+    7  =  15 

9+    7  =  16 

10+    7  =  17 

8+    8  =  16 

9+    8  =  17 

10+    8  =  18 

8+    9  =  17 

9+    9  =  18 

10+    9  =  19 

8  +  10  =  18 

9  +  10  =  19 

10  +  10  =  20 

8  +  11  =  19 

9  +  11  =  20 

10  +  11=21 

8  +  12  =  20 

9  +  12  =  21 

10  +  12  =  22 

LESSON  IV. 


1.  Three  and  8  are  how  many?     6  and  9? 

2.  Four  and  4  are  how  many?     4  and  11? 

4  and  12? 

3.  Five  and  9  are  how  many? 

5  and  8?     5  and  11?     6  and  6? 

4.  Seven  and  7  are  how  many? 
7  and  12?    7  and  9?    7  and  11? 

5.  Nine  and  11  are  how  many? 
9  and  10?     9  and  8? 

6.  Ten    and    6   are   how   many? 
10?     10  and  12?     10  and  11? 

7.  Eleven  and  2  are  how  many?     11  and  4? 
6?     11  and  8?     11  and  3?     11  and  11? 

8.  Twelve  and  3  are  how  many?     12  and  4? 
6?     12  and  8?     12  and  11?     12  and  12? 


5  and  12? 

6  and  8? 

7  and  10? 

8  and  8? 

9  and  9? 


4  and  10? 


5  and  10? 


7  and  8? 


9  and  12? 


10  and  8?      10  and 


11  and 


12  and 


12  KAY'S    NEW    INTELLECTUAL   ARITHMETIC. 

9.  Thirteen    and   4   are   how  many?      13   and    6?     13 
and  5?     13  and  7?     13  and  9?     13  and  10?     13  and  8? 

13  and  11?     13  and  12? 

10.  Fourteen  and  four  are  how  many?     14  and  6?     14 
and  8?     14  and  5?     14  and  7?     14  and  10?     14  and  9? 

14  and  11?     14  and  12? 

11.  Fifteen    and    5    are    how   many?     15    and    7?     15 
and  9?     15  and  4?     15  and  8?     15  and  10?     15  and  12? 

15  and  11? 

12.  Sixteen    and   4    are    how   many?     16    and   6?     16 
and  8?     16  and  5?     16  and  7?     16  and  9?     16  and  11? 

16  and  10?     16  and  12? 

13.  Seventeen  and  6  are  how  many?     17  and  4?     17 
and  7?     17  and  5?     17  and  9?     17  and  8?     17  and  10? 

17  and  12?     17  and  11? 

14.  Eighteen  and  10  are  how  many?     18  and  4?     18 
and  7?    18  and  5?     18  and  8?     18  and  6?     18  and  9? 

18  and  11?     18  and  12? 

15.  Nineteen   and   5   are   how  many?     19  and  3?     19 
and  2?     19  and  7?     19  and  9?     19  and  8?     19  and  10? 

19  and  6?     19  and  12?     19  and  11? 

16.  How  many  arc  29  and  2?     49  and  2?     69  and  2? 
39  and  2?    59  and  2?    79  and  2?     99  and  2? 

17.  How  many  are  29  and  3  ?     3  and  49  ?     59  and  3  ? 
3  and  39?     69  and  3?    3  and  79?    3  and  89?     99  and  3? 

18.  How  many  are  29  and  7?    7  and  49?     39  and  7? 

7  and  59?    79  and  7?    7  and  69?    89  and  7?    7  and  99? 

19.  How  many  are  29  and  8  ?     49  and  8?     39  and  8? 

8  and  69?    59  and  8?    79  and  8? 

20.  How  many  are  19  and  9?     9  and  29?    49  and  9? 
69  and  9?     59  and  9?     79  and  9?     89  and  9?     9  and 
99? 

21.  How  many  are  28  and  3?    48  and  3?     68  and  3? 
88  and  3?    98  and  3? 


ADDITION.  13 

22.  How  many  arc  28  and  7?     7  and  38?     48  and  7? 
68  and  7?     58  and  7?     88  and  7? 

23.  How  many  are  17  and  7?     27  and  7?     47  and  7? 
57  and  7?     37  and  7?     67  and  7?     87  and  7?     77  and  7? 
97  and  7? 

24.  How  many  are  27  and   10?     47  and    10?     37  and 
10?    57  and  10? 

25.  How  many  are  15  and  6?     26  and  5?     25  and  6? 
24   and   6?     26    and    4?     36    and    6?     48    and    6?     45 
and  6?     57  and  6?     59  and  6?     66  and  6?     75  and  6? 
86  and  6? 

26.  How  many  are  17  and  3?     23  and  8?     24  and  8? 
33  and  8?     3  and  37?     8  and  43?     47  and   3?     7  and 
53?    58  and  3?     67  and  3?    3  and  87?     97  and  3?     88 
and  3? 

27.  How  many  are  9  and  24?     25  and  9?     9  and  34? 
36  and  9?      9  and  44?      9  and  47?     54  and  9?     9  and 
56?    9  and  64?    74  and  9?    9  and  72?    84  and  9?    86 
and  9?     94  and  9? 

28.  How  many  are  6   and  21?      10  and  26?      46  and 
10?     10  and  35?     10  and  55?     56  and  10?     10  and  66? 

10  and  69?     76  and  10?     10  and  86?     96  and  10? 

29.  How  many  are  11   and   16?     11  and  27?     25  and 
11?     11  and  23?     31  and  11?     11  and  35?     37  and  11? 

11  and  59?     46  and  11?     11  and  48?     52  and  11?     11 
and  63? 

LESSON  V. 

1.  Three  and  6  and  4  are  how  many? 
SOLUTION. — Three  and  six  are  nine,  and  four  arc  thirteen. 

2.  Four  and  5  and  7  are  how  many? 

3.  Five   and  6  and  2  are  how  many? 

4.  Six      and  4  and  5  are  how  many? 


14        RAY'S    NEW   INTELLECTUAL  ARITHMETIC. 

5.  Seven  and  3  and  5  and  2  are  how  many? 

6.  Eight  and  2  and  3  and  4  are  how  many? 

7.  Nine     and  2  and  4  and  3  are  how  many? 

8.  Two     and  8  and  5  and  4  are  how  many? 

9.  Three  and  9  and  5  and  4  are  how  many? 

10.  Four  and  8  and  3  and  5  and  2  and  6  and  3  and 

1  are  how  many? 

11.  Five  and  7  and  2  and  3  and  4  and  6  and  5  and 

2  are  how  many? 

12.  Two  and  4  and  3  and  5  and  6  and  2  and  7  and 
4  are  how  many? 

13.  Three  and  2  and  4  and  5  and  4  and  6  and  3  and 

7  and  5  are  how  many? 

14.  Four  and  3  and  5  and  7  and  6  and  8  and  2  and 

4  are  how  many? 

15.  Four  and  9  and  3  and  5  and  6  and  7  and  8  and 
9  are  how  many? 

16.  Five  and  8  and  5  and  8  and  5  and  8  and  5  and 

8  are  how  many? 

17.  Six  and  8  and  7  and  3  and  5  and  4  and  7  and  1 
and  9  are  how  many? 

18.  Seven  and  9  and  5  and  4  and  6  and  3  and  8  and 

5  and  9  are  how  many? 

19.  Eight  and  7  and  6  and  5  and  4  and  9  and  3  and 
7  and  8  are  how  many? 

20.  Nine  and  6  and  7  and  4  and  5  and  3  and  8  and 
2  and  9  are  how  many? 

21.  Seven  and  6  and  5  and  8  and  7  and  9  and  8  and 
4  and  9  and  8  are  how  many? 

22.  Nine  and  8  and  7  and  5  and  8  and  9  and  5  and 
4  and  7  and  3  and  9  and  8  are  how  many? 

23.  Twelve  and  11  and  7  and  4  and  9  are  how  many? 

24.  Thirteen  and   10  and   8  and   0  and  4  and   10  are 
how  many? 


ADDITION.  15 

25.  Fourteen  and  16  and  7  and  5  and  9  and  8  and  9 
and  6  and  4  are  how  many? 

26.  James   gave   7    cents   for  apples,  and    8   cents   for 
peaches:  how  many  cents  did  he  spend? 

SOLUTION. — He  spent  7  cents  and  8  cents,  which  are  15  cents. 

27.  Seven  dollars  and  5  dollars  and  3  dollars  are  how 
many  dollars? 

28.  David  had  11  books;   he  bought  7  more,  and  his 
brother  gave  him  5 :  how  many  had  he  then  ? 

29.  A  man  gave   13  dollars  for  a  cart,  9  dollars  for  a 
plow,  and  1  dollar  for  a  rake :   how  much  did  he  spend  ? 

30.  James  has  8   marbles  in  one  pocket,  5  in  another, 
6  in  another,  and  7  in  another:  how  many  in  all? 

31.  If  a  dozen  eggs  cost  18  cents,  and  a  pound  of  ham 
10  cents,  how  much  will  both  cost? 

32.  A  man  owes  to  one  person  8  dollars,  to  another  5 
dollars,  to  another  3  dollars,  and  to  another  7  dollars: 
how  much  does  he  owe? 

33.  A  boy  gave  19  cents  for  a  spelling-book,  8  cents 
for  a  slate,  and  6  cents  for  pencils:  how  many  cents  did 
he  spend? 

34.  A  drover  bought  hogs  as  follows :   of  one  man  17, 
of  another  9,  of  another  7,  of  another  8 :   how  many  did 
he  buy? 

35.  A  little  girl  gave  10  cents  for  thread,  7  cents  for 
pins,  6  cents  for  needles,  and  9  cents  for  tape :  how  many 
cents  did  she  spend? 

36.  William   has   7  cents,   Thomas    10    cents,  David    9 
cents,  and  Moses  8  cents :    if  the  other  boys  give  their 
money  to  Moses,  how  many  cents  will  he  have  ? 

37.  The  age  of  Thomas  is  8  years;  of  Frank,..  5.  years; 
and  William  is  as  old  as  both  together:  what  is  the  sum 
of  all  their  ages? 


16        RAY'S    NEW    INTELLECTUAL   ARITHMETIC. 

38.  Joseph  has  4  marbles,  William  has  2,  and  David 
has  16:  how  many  have  they  all? 

39.  Begin  with  2,  and  count  one  hundred  by  adding  2 
successively.     Thus,  2,  4,  6,  8,  10,  and  so  on. 

40.  Begin  with  3,  and  count  ninety-nine  by  adding  3 
successively.     Thus,  3,  6,  9,  12,  and  so  on. 

41.  Begin  with  4,  and    r-ount  one  hundred  by  adding 

4  successively. 

42.  Begin  with   5,  and   count  one  hundred  by  adding 

5  successively. 

43.  Begin  with  6,  and  count  one  hundred  and  two  by 
adding  6  successively. 

44.  Begin  with  7,  and  count   ninety-eight  by  adding 
7  successively. 

45.  Begin  with  8,  and  count  one  hundred  and  four  by 
adding  4  successively. 

46.  Begin  with  9,  and  count  ninety-nine  by  adding  9 
successively. 

47.  Begin  with  1,  and  count  one  hundred  by  adding  3 
successively. 

48.  Begin  with  3,  and  count  one  hundred  and  three  by 
adding  4  successively. 

49.  Begin  with  2,  and  count  one  hundred  and  two  by 
adding  5  successively. 

50.  Begin  with  5,  and  count  one  hundred  and  seven  by 
adding  6  successively. 

51.  Begin  with  6,  and  count  one  hundred  and  four  by 
adding  7  successively. 

52.  Begin  with  7,  and  count  one  hundred  and  three  by 
adding  8  successively. 

53.  Begin  with  8,  and  count  one  hundred  and  seven  by 
adding  9  successively. 


LESSON;  vi. 

1.  James    had   2   apples,   and   gave   1    to   his   brother: 
how  many  had  he  loft?     Ans.  1. 

Why?    Ans.  Because  1  from  2  leaves  1. 

2.  Joseph  had  3  apples  and  lost  1 :   how  many  had  ho 
left?    Ans.  2. 

Why?    Ans.  Because  1  from  3  leaves  2. 

3.  Thomas  had  4  cents,  and  gave  1  of  them  to  Frank  : 
how  many  had  he  left? 

4.  One  from  5  leaves  how  many?     From  6?     7?     8? 
9?     10? 

5.  John  had  4  cents  and  gave  his  sister  2 :   how  many 
had  he  left? 

6.  James  had   5  apples,  and  gave  his  brother  2 :    how 
many  had  he  left? 

7.  Two  from  6  leaves  how  many?     From  7?     8?     9? 
10?     11? 

8.  Thomas  had  5  cents  and  lost  3 :  how  many  had  ho 
left? 

9.  Three  from  6  leaves  how  many?     From  7?     8?     9? 
10?     11?     12? 

10.  Joseph  had  9  marbles  and  lost  4 :    how  many  had 
he  left? 

11.  Four  from  10    leaves  how  many?     From  11?     12? 
13?     14?     15? 

12.  William    had    10  apples  and  gave  Joseph   5:    how 
many  had  he  left? 

Int.  2.  (17) 


18        RAY'S    NEW   INTELLECTUAL  ARITHMETIC. 

13.  Five  from  11   leaves  how  many?     From  12?     13? 
14?     15?     16? 

14.  James  had  11  marbles  and  lost  6 :   how  many  had 
he  left? 

15.  Six   from   12    leaves  how  many?     From    13?     14? 
15?     16?     17? 

16.  William  had   12  cents  and   lost  7 :    how  many  had 
he  left? 

17.  Seven  from  13  leaves  how  many?     From  14?     15? 
16?     17?     18?     19? 

18.  James  had   13  apples  and  gave  his  sister  8 :    how 
many  had  he  left? 

19.  Eight  from  14  leaves  how  many?     From  15?     16? 
17?     18?     19?    20? 

20.  Thomas  had  13  apples  and  gave  his  sister  9 :   how 
many  had  he  left? 

21.  Nine  from  14  leaves  how  many?    From  15?     16? 
17?     18?     19?     20? 

22.  Henry  had  17  cents  and  lost  5 :  how  many  had  he 
remaining? 

23.  Mary  is   12  years  old,  and  Anna  is  8:   how  much 
older  is  Mary  than  Anna? 

24.  Sold  a  load  of  corn  for  17  dollars ;  received  for  it 
a  barrel  of  flour  worth  6  dollars,  and  the  rest  in  money : 
how  much  money  did  I  receive? 

25.  A  boy  had  18  marbles  and  lost  10 :  how  many  had 
he  then? 

Subtraction  is  the  process  of  finding  the  difference  be- 
tween two  numbers. 

The  larger  number  is  called  the  minuend;  the  smaller 
number,  the  subtrahend;  and  the  result,  the  difference  or 
remainder, 

The  sign  of  subtraction  ( — )  is  called  minus. 


SUBTRACTION. 


19 


LESSON  VII. 


SUBTRACTION  TABLE. 


i 

2  —  2=  0 

3  —  3=  0 

4  —  4=  0 

3  —  2  =  1 

4  —  3=  1 

5  —  4=  1 

4  —  2=  2 

5  —  3=  2 

6  —  4=  2 

5  —  2  =  3 

6  —  3=  3 

7—4=  3 

6  —  2=  4 

7  —  3=  4 

8  —  4=  4 

7  —  2=  5 

8  —  3=  5 

9  —  4=  5 

8  —  2=  6 

9  —  3=  6 

10  —  4=  6 

9  —  2=  7 

10  —  3=  7 

11—4=  7 

10-2=  8 

11—3=  8 

12  —  4=  8 

11—2=  9 

12  —  3=  9 

13  —  4=  9 

12  —  2  =  10 

13  —  3  =  10 

14  _  4  =  10 

13  —  2  =  11 

14  —  3  =  11 

15  —  4  =  11 

14  —  2  =  12 

15  —  3  =  12 

16  —  4  =  12 

5  —  5=  0, 

6  —  6=  0 

7  —  7=  0 

6  —  5=  1 

7-6=  1 

8  —  7=  1 

7  —  5=  2 

8  —  6=  2 

9  —  7=  2 

8  —  5=  3 

9  —  6=  3 

10  —  7=  3 

9  —  5=  4 

10  —  6=  4 

11—7=  4 

10  —  5=  5 

11  —  6=  5 

12  —  7=  5 

11  —  5=  6 

12  —  6=  6 

13  —  7=  6 

12  —  5=  7 

13  —  6=  7 

14  —  7=  7 

13  —  5=  8 

14_6=  8 

15  —  7=  8 

14  —  5  =  9 

15  —  6=  9 

16  —  7=  9 

15  —  5  =  10 

16  —  6  =  10 

17  —  7  =  10 

16  —  5  =  11 

17  —  6  =  11 

18-7  =  11 

17  —  5  =  12 

18  —  6  =  12 

19  —  7  =  12 

20        KAY'S    NEW   INTELLECTUAL  ARITHMETIC. 


8  —  8=  0 

9  —  9=  0 

10  —  10=  0 

9  —  8=  1 

10  —  9=  1 

11  —  10=  1 

10  —  8=  2 

11—9=  2 

12  —  10=  2 

11  —  8=  3 

12  —  9=  3 

13  —  10=  3 

12  —  8=  4 

13  —  9=  4 

14  —  10=  4 

13  —  8=  5 

14  —  9^  5 

15  —  10=  5 

14  —  8=  6 

15  —  9=  6 

16—10=  6 

15  —  8=  7 

16  —  9=  7 

17  —  10=  7 

16  —  8=  8 

17—9=  8 

18  —  10=  8 

17  —  8=  9 

18  —  9=  9 

19  —  10=  9 

18  —  8  =  10 

19  —  9  =  10 

20  —  10  =  10 

19  —  8  =  11 

20  —  9  =  11 

21  —  10  =  11 

20  —  8  =  12 

21  —  9  =  12 

22  —  10  =  12 

LESSON   VIII. 


1.  A  boy  gave  9  cents  for  a  slate,  worth  only  7  cents: 
how  much  did  he  pay  for  it  more  than  it  was  worth? 

SOLUTION. — He  paid  more  than   it  was  worth   the   difference  be- 
tween 9  cents  and  7  cents,  which  is  2  cents. 

2.  A  man,  having  16  dollars,  lost  12 :   how  many  dol- 
lars had  he  left? 

3.  Bought  a  book  for  12  cents,  and  a  top  for  7  cents: 
how  much  did  the  book  cost  more  than  the  top? 

4.  Thomas  had  18  cents  given  him  by  two  boys;   one 
gave  9:   how  many  did  the  other  give? 

5.  Bought   a   book   for  14   cents,  and   gave   the   shop- 
keeper 20  cents :  how  much  change  did  he  return  me  ? 

6.  William   has   19  hazel-nuts   in   his  two  pockets;    in 
one  pocket  he  has  15:   how  many  are  in  the  other? 


SUBTRACTION.  21 

7.  A  man  has  25  miles  to  travel :  when  he  has  gone 
19  miles,  how  far  will  he  still  have  to  travel? 

8.  A  boy  gave  24  cents  for  a  book,  and  sold  it  for  16 
cents :   how  much  did  he  lose  ? 

9.  James  had  24  marbles;    he  gave  19   to  his  brother: 
how  many  had  he  left? 

10.  A  man  bought  a  horse  for  19  dollars,  and  sold  him 
for  27  dollars :  how  much  did  he  gain  ? 

11.  A  man,  owing  26  dollars,  paid  18;    how  many  did 
he  still  owe? 

12.  Frank   had    26   cents  given   him   by  William    and 
Thomas.     William  gave  him  17 :   how  many  did  Thomas 
give?    How  many  more  did  William  give  than  Thomas? 

SOLUTION. — Thomas  gave  him  26  cents  less  17  cents,  which  are  9 
cents;  William  gave  more  than  Thomas  17  cents  less  9  cents,  which 
are  8  cents. 

13.  If  you  had  10  apples,  and  should  give  2  to  John, 
and  6  to  your  sister:  how  many  would  you  have  left? 

14.  Abel  had  36  cents,  and  his  mother  gave  him  enough 
more  to  make  40  cents :  how  many  did  she  give  him  ? 

15.  George  had  40  marbles ;  he  lost  20 :  how  many  did 
he  then  have? 

16.  A  man  bought  100  barrels  of  flour;  he  sold  50  bar- 
rels :  how  many  did  he  have  left  ? 

17.  A  farmer  had  35  bushels  of  grain ;  a  part  having 
been  wasted,  he  found  there  were  but  22  bushels  remain- 
ing :  how  much  was  wasted  ? 

18.  John's  father  is  36  years  old ;  John  is  12 :  how  many 
years  older  than  John  is  his  father  ? 

19.  I  had  65  cents ;   spent  20  cents  for  a  book  and  10 
for  a  slate :  how  much  had  I  left  ? 

20.  If  you  take  10  from  the  sum  of  two  numbers,  there 
will  be  8  left:  what  is  their  sum? 


22        RAY'S    NEW   INTELLECTUAL  ARITHMETIC. 

21.  If  you  take  16  from  the  difference  of  two  numbers, 
there  will  remain  12:  what  is  their  difference? 

22.  The  sum  of  two  numbers  is  20 :  what  number  must 
be  added  to  make  their  sum  30? 

23.  The  sum  of  two  numbers  is  16  more  than  their 
difference ;  if  their  difference  is  4,  what  is  their  sum  ? 

24.  The  greater  of  two  numbers  is  12,  and  their  differ- 
once  5 :  what  is  the  less  ? 

25.  The  sum  of  two  numbers  is  21 ;  the  less  number  is 
8:  what  is  the  greater? 


LESSON  IX. 
REVIEW. 

1.  James  had  13  marbles;  he  gave  2  to  Henry,  and  3  to 
Thomas :  how  many  had  he  left  ? 

SOLUTION. — James  gave  away  2  marbles  and  3  marbles,  which  are 
5  marbles;  then  he  had  left  13  marbles  less  5  marbles,  which  are 

8  marbles. 

2.  A  merchant  had  40  barrels  of  flour;  he  sold  to  one 
man  9,  to  another  21 :  how  many  had  he  left  ? 

3.  On  Christmas  day,  William  had  36  cents  given  him ; 
ho  spent  6  cents  for  apples,  9  cents  for  cakes,  and  10  cents 
for  candy:  how  many  had  he  left? 

4.  A  man  paid  30  dollars  for  a  horse,  the  keeping  cost 

9  dollars,  and  he  sold  him  for  29  dollars :  how  many  dol- 
lars did  he  lose? 

5.  A  man,  having  34  dollars,  bought  a  barrel  of  molasses 
for  15  dollars,  and  a  bag  of  coffee  for  10  dollars :  how 
many  dollars  had  he  left? 


SUBTRACTION.  23 

6.  A  grocer  bought  some  oranges  for  9  dollars,  some 
lemons  for  7  dollars,  some  prunes  for  5  dollars,  and  some 
figs  for  9  dollars ;   he  then  sold  them  for  41  dollars :  how 
much  did  he  gain? 

7.  A  lady  bought  a  comb  for  25  cents,  some  pins  for  10 
cents,  tape  for  7  cents,  thread  for  6  cents,  arid  a  toy-book 
for  5  cents ;    she  gave  60  cents  to  the  shop-keeper :    how 
much  change  ought  she  to  receive? 

8.  Two  boys  commenced  playing  marbles;  each  had  18 
when  they  began ;  when  they  quit,  one  had  25 :  how  many 
had  the  other? 

SOLUTION. — When  they  began,  both  had  18  marbles  and  18  mar- 
bles, which  are  36  marbles;  then,  when  they  quit,  the  other  had  36 
marbles  less  25  marbles,  which  are  11  marbles. 

9.  Thomas  has  7  marbles,  David  5,  and  Moses  11 ;  how 
many  have   they  all?      How  many  more   than   Thomas 
have  Moses  and  David  together? 

10.  Three  boys  played  marbles :  Thomas  had  20,  David 
10,  and  Moses  4;  when  they  quit,  David  had  6  and  Moses 
12  :  how  many  had  Thomas? 

11.  A  farmer  had  24  sheep;   9  of  them  were  killed  by 
wolves,  5  of  them  were  stolen,  and  6  he  sold :  how  many 
had  he  left? 

12.  A  grocer  bought   sugar  for  12  dollars,  flour  for  6 
dollars,  and  coffee  for  5  dollars ;  he  sold  the  whole  for  30 
dollars :  how  much  did  he  make  ? 

13.  A  lady  had  50  cents ;  she  spent  25  cents  for  butter, 
and  10  cents  for  eggs:  how  much  had  she  left? 

14.  A  man  is  indebted  to  A,  5  dollars ;  to  B,  6  dollars ; 
and  to   C,  10  dollars :    he  has  cash  to  the  amount  of  20 
dollars,  and  goods  valued  at  10  dollars :  should  he  pay  his 
debts,  how  much  would  he  be  worth  ? 

15.  How  many  are  90  less  35,  less  25,  less  15? 


24        HAY'S    NEW   INTELLECTUAL   ARITHMETIC. 


LESSON  X. 


SOLUTION.  —  3  minus  2  plus  1  equals  2, 

2.  4—3  +  2=? 

3.  6  —  5-|-4=? 

4.  8  —  7  +  6=? 

5.  7  —  3  +  5=? 

6.  9  —  4  +  7=? 

7.  4_3_|_2  —  1=? 

8.  6-5  +  4  —  3=? 

9.  8  —  4  +  6  —  5=? 

10.  9_5  +  7  —  2=? 

11.  9_4  +  3_2  +  1=? 

12.  8  —  5  +  4  —  3  +  2=? 

13.  7_3+5_4+3=? 

14.  8  —  2  +  6  —  5  +  4=? 

15.  9__5  +  7_6  +  5=? 

16.  6  —  2  +  4  —  3  +  2  —  1=? 

17.  7  —  4  +  5  —  4  +  3  —  2=? 

18.  8  —  5  +  6  —  5  +  4  —  3=? 

19.  9_  6  +  7  —  6  +  5  —  4=? 

20.  7  —  6  +  5  —  4  +  3  —  2  +  1^? 

21.  8  —  6  +  6  —  5  +  4  —  3+2  —  1=? 

22.  9  —  5  +  7  —  6  +  5—4  +  3  —  2  +  1=? 

23.  1  +  2  +  3  —  4  +  5  —  6  +  7  —  5  +  9=? 

24.  9  —  1—2  —  3  +  4  —  5  +  6  —  4  +  8=? 

25.  1  +  9  —  2  —  3  +  3  +  7  —  6  —  4  +  5=? 

26.  9  —  7  +  8  —  5  +  6  —  3  +  4  —  2  +  1  —  10=? 

27.  i       3_2       4-5  +  7  —  6  +  8  —  9  +  10=? 


SUBTRACTION.  25 

LESSON  XI. 

1.  Henry  had  24  cents,  and  spent  all  but  15 :  how  many 
did  he  spend? 

2.  A  man  bought  a  cask  of  wine  containing  27 gallons; 
after  selling  10  gallons,  he  found  there  were  but  9  gallons 
remaining,  the  rest  having  leaked  out:  how  much  did  he 
lose? 

3.  If  from   20  you  take   12  less  3,   how  many  will  re- 
main? 

4.  If  from  the  sum  of  19  and  10  you  take  the  difference 
between  17  and  10,  what  will  be  left? 

SOLUTION. — 19   plus   10  equals    29;    17   minus    10   equals   7;   29 
minus  7  equals  22. 

5.  A  man  owed  60  dollars :  he  paid  at  one  time  20  dol- 
lars, and  at  another  30  dollars ;  he  afterwards  borrowed  5 
dollars :  how  much  does  he  still  owe  ? 

6.  A    man    paid    38   dollars    for   a    horse,   and    20   for 
a   colt:    he   afterwards   sold   the  colt  for  10  dollars,  and 
the    horse    for    65 :    how    much    did    he    make    by   the 
transaction  ? 

7.  Twenty-four  less  8,  and  12  less  5,  are  together  how 
much  less  than  25? 

8.  Engaged  to  do  a  piece  of  work  for  60  dollars :  had  an 
assistant  25  days  at  a  dollar  a  day,  and  paid  20  dollars  for 
materials :  how  much  did  I  earn  ? 

9.  If  from  the  sum  of  8  and  9  and  10  and  11,  you  take 
the  sum  of  4  and  5  and  6  and  7,  what  will  you  have  re- 
maining? 

10.  A  jeweler  bought  a  watch  for  40  dollars,  a  chain  for 
15  dollars,  and  a  key  for  3  dollars :   he  sold  them  for  63 
dollars :  what  did  he  gain  ? 


26        KAY'S    NEW  INTELLECTUAL  ARITHMETIC. 

11.  A   drover  bought  sheep  as   follows  :    of  one   man, 
10 ;    of  another,   12 ;    of  another,  5 ;    of  another,  3 :    he 
sold   at   one  time,   15 ;    and    at    another,  5  :    how  many 
were   left  ? 

12.  A  gentleman,  having  40  dollars,  purchased  a  suit  of 
clothes :  his  pants  cost  7  dollars ;  vest,  5  dollars ;  coat,  25 
dollars :  how  much  had  he  left  ? 

13.  What  number  must  be  added  to  25  to  make  a  sum 
14  less  than  4§? 

14.  What  number  must  be   taken   from   62   to   give   a 
result  which  shall  be  12  more  than  45? 

15.  If  from  the  sum  of  25  and  10  and  12,  you  take  the 
difference  between  28  and  19,  what  will  remain? 

16.  A  man   bought   a  horse  for  40   dollars :    and,  after 
paying  15  dollars  for  keeping  him,  sold  him  for  75  dollars: 
how  much  did  he  make? 

17.  A  gentleman  engaged  in  trade  with  75  dollars :  after 
losing  at  one  time  10  dollars,  and  at  another  5,  he  gained 
20  dollars :  how  much  did  he  then  have  ? 

18.  The   difference    between    two    numbers   is   17 :    the 
greater  number  is  85 :  what  is  the  less  ? 

19.  John  and   James  entered   into  partnership  in  busi- 
ness, with  a  joint  capital  of  100  dollars.     John  furnished 
60  dollars  of  the  money:  what  was  James's  share? 

20.  A  barrel  contained  30  gallons  of  syrup.     Of  this, 
14  gallons  were   sold,  5  gallons   leaked  out,  and  3  gal- 
lons were  given  away :  how  much  syrup  remained  in  the 
barrel? 

21.  An    orchard    contains,   in    one    row,  5   apple  trees 
and  15  peach  trees;    in  another  row,  11  apple  trees  and 
9   peach   trees ;    and  in   another,  10  trees  of  each  kind : 
how  many  more  peach  trees  in  the  orchard  than  apple 
trees  ? 

22.  How  many  arc  87  less  14,  less  21,  less  51? 


LESSON  XII. 

1.  A  boy  gave  2  cents  for  one  lemon,  and  2  cents  for 
another:   how  many  cents  did  he  give  for  both?     Ans.  4 
cents. 

Why  ?    Ans.  Because  2  times  2  are  4. 

2.  A  boy  gave  3  cents  for  one  peach,  and  3  cents  for 
another :  how  many  cents  did  he  give  for  both  ? 

3.  At  4  cents  apiece,  what  wrill  2  pears  cost? 

4.  At  3  cents  apiece,  what  will  3  peaches  cost? 

5.  At  3  cents  apiece,  what  will  4  apples  cost? 

6.  At  3  cents  apiece,  what  will  5  postage  stamps  cost? 

7.  At  4  cents  apiece,  what  will  4  lemons  cost? 

8.  At  5  dollars  a  yard,  what  will  4  yards  of  cloth  cost? 

9.  At   6   dollars  a  barrel,  what  will  4   barrels  of  flour 
cost? 

10.  At  5  cents  apiece,  what  will  5  bananas  cost? 

11.  At  6  cents  a  yard,  what  will  5  yards  of  tape  cost? 

12.  At  6  cents  apiece,  what  will  6  oranges  cost? 

13.  At  7  cents  a  yard,  what  will  2  yards  of  calico  cost? 

14.  At  7  cents  apiece,  what  will  3  papers  cost? 

15.  At  7  cents  apiece,  what  will  4  toys  cost? 

16.  If  1  marble  is  worth  7  apples,  how  many  apples  are 
5  marbles  worth? 

17.  If  1  peach  is  worth  8  apples,  how  many  apples  are 

2  peaches  worth? 

(27) 


28        KAY'S    NEW   INTELLECTUAL  ARITHMETIC. 

18.  If  1   orange  cost  8  cents,  how  many  cents  will  3 
oranges  cost?     4  oranges? 

19.  If  1  orange  is  worth  8  apples,  how  many  apples  are 
5  oranges  worth  ? 

20.  At  9   cents  a  yard,  what  will    2   yards   of  calico 
cost?    3  yards? 

21.  What  will  4  quarts  of  nuts  cost,  at  10  cents  a  quart? 

22.  What  will  3  yards  of  muslin  cost,  at  11  cents  a  yard? 

Multiplication  is  taking  one  number  as  many  times  as 
there  are  units  in  another. 

The  multiplicand  is  the  number  to  be  taken.  The  mul- 
tiplier is  the  number  denoting  how  many  times  the 
multiplicand  is  to  be  taken.  The  product  is  the  result. 

The  sign  of  multiplication  (X)  is  read  multiplied  by. 


LESSON  XIII. 
MUL  TIPLICA  TION    TA BLE. 


ixi=  i 

1X2=    2 

1X3=    3 

2X1=    2 

2X2=    4 

2X3=6 

3X1=3 

3X2=    6 

3X3=    9 

4X1=    4 

4X2=    8 

4X3  =  12 

5X1=5 

5  X  2  =  10 

5  X  3  =  15 

6X1=    6 

6X2  =  12 

6  X  3  =  18 

7X1=7 

7  X  2  =  14 

7  X  3  =  21 

8X1=    8 

8  X  2  =  16 

8  X  3  =  24 

9X1=9 

9  X  2  =  18 

9  X  3  =  27 

10  X  1  =  10 

10  X  2  =  20 

10X3  =  30 

11x1  =  11 

11  X  2  =  22 

11  X  3  =  33 

12X1  =  12 

12  X  2  =  24 

12  X  3  =  36 

MULTIPLICATION. 


29 


1X4=    4 

1X5=5 

1X6=      6 

2X4=    8 

2  X  5  =  10 

2X6=    12 

3X4  =  12 

3  X  5  =  15 

3X6=    18 

4  X  4  =  16 

4  X  5  =  20 

4X6=    24 

5  X  4  =  20 

5  X  5  =  25 

5X6=    30 

6  X  4  =  24 

6  X  5  =  30 

6X6=    36 

7  X  4  =  28 

7  X  5  =  35 

7X6=    42 

8  X  4  =  32 

8  X  5  =  40 

8X6=    48 

9  X4  =  36 

9  X  5  =  45 

9X6=    54 

10  X  4  =  40 

10  X  5  =  50 

10  X  6=    60 

11  X  4  =  44 

11  X  5  =  55 

11  X  6=    66 

12  X  4  =  48 

12  X  5  =  60 

12  X  6=    72 

1X7=7 

1X8=8 

1X9=      9 

2  X  7  =  14 

2  X  8  =  16 

2X9=    18 

3X7  =  21 

3  X  8  =  24 

3X9=    27 

4  X  7  =  28 

4  X  8  =  32 

4X9=    36 

5  x  7  =  35 

5  X  8  =  40 

5X9=    45 

6  X  7  =  42 

6  X  8  =  48 

6X9=    54 

7  X  7  =  49 

7  X  8  =  56 

7X9=    63 

8  X  7  =  56 

8  X  8  =  64 

8X9=   72 

9  X  7  =  63 

9  X  8  =  72 

9X9=    81 

10  X  7  =  70 

10  X  8  =  80 

10  X  9  =    90 

11  x  7  =  77 

11  X  8  =  88 

11  X  9=    99 

12  X  7  =  84 

12  X  8  =  96 

12  X  9  =  108 

30        RAY'S    NEW   INTELLECTUAL   ARITHMETIC. 


1  X  10=  10 

i  xii=  11 

1  X  12=  12 

2x  10=  20 

2  X  11  =  22 

2  X  12  =  24 

3  X  10=  30 

3  X  H=  33 

3X12=  36 

4  X  10  =  40 

4  X  11  —  44 

4  X  12  =  48 

5  X  10=  50 

5x11=  55 

5  X  12=  60 

6  x  10=  60 

G  X  H=  66 

6  X  12  =  72 

7  x  10  =  70 

7  x  11=  77 

7  X  12  =  84 

8  x  10=  80 

8xH=  88 

8  X  12  =  96 

9  x  10=  90 

9  X  H=  99 

9  X  12  =  108 

10  X  10  =  100 

10  X  11  =  110 

10  X  12  =  120 

11  X  10  =  110 

11  X  11  =  121 

11  X  12  =  132 

12  X  10  =  120 

12  X  11  =  132 

12  X  12  =  144 

EXERCISES  ON  THE   TABLE. 

1.    4  times  7  arc  how  many? 
SOLUTION. — 4  times  7  are  28. 


2. 

8 

times 

2? 

7 

times 

5? 

6 

times 

7? 

3. 

8 

times 

6? 

6 

times 

9? 

9 

times 

7? 

4. 

9 

times 

8? 

7 

times 

7? 

7 

times 

8? 

5. 

12 

times 

2? 

2 

times 

10? 

3 

times 

6? 

6. 

10 

times 

5? 

4 

times 

11? 

12 

times 

3? 

7. 

8 

times 

8? 

6 

times 

11? 

9 

times 

2? 

8. 

7 

times 

10? 

12 

times 

4? 

8 

times 

5? 

9. 

3 

times 

2? 

4 

times 

2? 

5 

times 

2? 

10. 

4 

times 

3? 

7 

times 

2? 

5 

times 

3? 

11. 

5 

times 

4? 

6 

times 

6? 

11 

times 

2? 

12. 

8 

times 

3? 

5 

times 

5? 

11 

times 

3? 

13. 

10 

times 

6? 

6 

times 

12? 

10 

times 

3? 

14. 

9 

times 

12? 

9 

times 

4? 

4 

times 

10? 

MULTIPLICATION. 


31 


15.  11  times  10? 

16.  9  times     5? 

17.  11  times  12? 

18.  8  times  10? 


10  times  12? 
9  times     9? 

11  times     5? 
7  times  12? 


8  times  12? 

11  times  11? 

5  times  12? 

8  times  11? 


19.  11  times     9?     10  times  10?     12  times  11? 


LESSON  XIV. 


1.  At  2  cents  each,  what  will  7  oranges  cost? 
SOLUTION. — 7  oranges  will  cost  7  times  2  cents,  which  are  14  cents. 

2.  At  7  cents  each,  what  will  3  melons  cost? 

3.  At  6  cents  a  dozen,  what  will  5  dozen  apples  cost? 

4.  At  8  cents  a  pound,  what  will  7  pounds  of  beef  cost? 

5.  At  $6  a  pound,  what  will  8  pounds  of  opium  cost? 

NOTE. — The  sign  $  means  dollars:    thus,  $6  is  read  G  dollars. 

6.  At  $3  a  barrel,  what  will  9  barrels  of  cider  cost? 

7.  At  $4  a  pair,  what  is  the  cost  of  7  pairs  of  boots  ? 

8.  At  8  cents  a  dozen,  what  will  10  dozen  pens  cost? 

9.  What  is  the  cost  of  6  yards  of  cloth  at  $7  a  yard  ? 

10.  What  do  8  barrels  of  flour  cost  at  $5  a  barrel? 

11.  If  a  man  travel  7  miles  an  hour,  how  far  will   he 
travel  in  8  hours? 

SOLUTION. — He  will   travel   8  times  7  miles,  which  are  66  miles. 

12.  On    a    chess-board   arc   8   rows   of  squares,  and    8 
squares  in  each  row:  how  many  squares  on  the  board? 

13.  An  orchard  has  11   rows  of  trees,  and  7  trees  in 
each  row:  how  many  trees  in  the  orchard? 

14.  What  will  9  yards  of  cloth  cost  at  $6  a  yard? 

15.  What  will  9  oranges  cost  at  8  cents  each? 


32        KAY'S    NEW   INTELLECTUAL   ARITHMETIC. 

16.  What  will   8   quarts  of  berries  cost  at  12   cents  a 
quart  ? 

17.  Two  men  start  from  the  same  place  and  travel  in 
opposite    directions :    one    travels    2    miles   an    hour,  the 
other  4  miles  an  hour :  how  far  will  they  be  apart  at  the 
end  of  3  hours? 

SOLUTION. — At  the  end  of  1  hour  they  will  be  2  miles  plus  4 
miles,  equal  6  miles,  apart;  then,  at  the  end  of  3  hours  they  will 
be  3  times  6  miles,  equal  18  miles,  apart. 

18.  If  2  men  can  do  a  job  of  work  in  3  days,  how  many 
days  will  it  take  1  man  to  do  it  ? 

SOLUTION. — It  will  take  1  man  2  times  3  days,  which  are  6  days. 

19.  If  3  men  can  do  a  piece  of  work  in  4  days,  in  how 
many  days  can  1  man  do  it  ? 

20.  If  4  men  can  do  a  piece  of  work  in  6  days,  in  how 
many  days  can  1  man  do  it? 

21.  If  a  quantity  of  bread   serve  8  men  4  days,  how 
many  days  will  it  serve  1  man  ? 

22.  If  a  man  can  earn  $6  in  1  week,  how  many  dollars 
can  he  earn  in  8  weeks? 

23.  A  person  has  a  piece  of  work  which  7  men  can  do 
in  9  days ;   but  it  is  necessary  to  have  it  done  in  1  day : 
how  many  men  must  be  employed? 

24.  If  $9  worth  of  provisions  last  8  persons  11  days, 
how  many  persons  will  it  last  1  day? 

25.  I  bought  6  barrels  of  apples  at  $2  a  barrel,  and  4 
barrels  of  sugar  at  $11  a  barrel:  how  much  did  they  both 
cost? 

SOLUTION.— The  apples  cost  6  times  $2,  equal  $12;  the  sugar  cost 
4  times  $11,  equal  $44;  then,  both  cost  $12  plus  $44,  equal  $56. 


MULTIPLICATION:  33 

LESSON  xv. 

1.  Bought   2   apples    at    2    cents   each,   2   pears   at  3 
cents  each,   and   an   orange   for   5    cents :    what  did  all 
cost? 

2.  Two  men    start    from  the  same  place  and  travel  in 
the  same  direction ;  one,  5    miles   an   hour ;    the  other,  7 
miles  an  hour:  how  far  will  they  be  apart  in  10  hours? 

3.  If,  in  the  above  question,  the  men  travel  in  opposite 
directions,  how  far  will  they  be  apart  in  12  hours? 

4.  A  lady  went  shopping  with  $15 ;  she  bought  4  yards 
of  cloth  at  $2  a  yard ;  2  pairs  of  gloves   at  $1   a  pair ; 
and  a  shawl  for  $2:    what  did   all   cost,  and   how  much 
had  she  left? 

5.  A   man   bought  4  peaches   at  5  cents  each,  3  pears 
at  3   cents   each,   and    2    pints  of  chestnuts  at  5  cents  a 
pint:  how  much  did  they  cost? 

6.  What  is  the  sum  of  3  and  9  and  7,  less  the  sum  of 
8  and  6  and  1? 

7.  If  a  man  earn  5  shillings  a  day,  and  a  boy  3  shil- 
lings, how  much  will  both  earn  in  7  days? 

8.  A  drover   gave    $10    and  7    sheep,  valued   at   $4    a 
head,  for  a  cow  and  calf:  how  much  did  they  cost? 

9.  A  merchant  sold  cloth  at  $7  a  yard :  a  tailor  bought 
of  this  cloth,   at    one    time,  5    yards,  and,  at   another,  3 
yards :  what  was  the  amount  of  his  bill  ? 

10.  Two  brothers,  Henry  and  Rufus,  each  received  for 
his  work  3  dimes  a  day :  how  much  did  both  receive  for 
6  days'  work? 

11.  If  12    horses    can    be    sustained    in    a    pasture    10 
months,  how  many  horses  will  it  feed  1  month? 

12.  What  is  3  times   the  difference  between  15  and  the 
sum  of  5  and  2? 

Int.  .« 


34        KAY'S    NEW   INTELLECTUAL   ARITHMETIC. 

13.  The  sum  of  two  numbers  is  23;  the  smaller  is  11: 
what  is  5  times  the  larger? 

14.  The  difference   between    two    numbers  is  7 :   if  the 
larger  be  12,  what  will  8  times  the  smaller  be? 

15.  If  a  boy  buy  10  cents   worth    of  apples  at  1  cent 
each,    and    sell  them   for    3   cents   each,  how   much    will 
he  make? 

16.  George  bought  a  book  for  50  cents  and  sold  it  for 
$1 :  'what  would    ho    have  made  had  he  bought  2  books, 
and  sold  them  at  the  same  rate  as  the  first? 

17.  Albert    has    5    times  2    marbles    less  than    50,  and 
Edward  has   5    times   2   more   than  50:    how   many  has 
each?    How  many  more  has  Edward  than  Albert? 

18.  If  $3  gain   $1   in   a  year,   what  will   $12  gain  in 
double  the  time? 

19.  A  man  bought  a  cask  of  wine    containing   20  gal- 
lons,  at    $1    a    gallon ;    5  gallons   having   leaked  out,   he 
sold    the   remainder    at   $2  a   gallon :    how  much  did  he 
make  ? 

20.  If  two    men  travel    in  the  same    direction,  one  10 
miles  and  the  other  7  miles  an   hour,  how  far  will  they 
be  apart  in  7  hours? 

21.  A  stage  starts  from  a  certain  town,  and  travels  at 
the  rate  of  8  miles  per  hour:  at  the  same  time,  another 
starts    from   the    same    place,   and    travels    in    the    same 
direction,  4  miles  per  hour:  how  far  will  they  be   apart 
at  the  end  of  12  hours? 

22.  A  grocer  bought  10  pounds  of  tea  at  7  shillings  a 
pound;    after  using   3  pounds,  he  sold  the   remainder  at 
10  shillings  a  pound:  how  much  did  the  3  pounds  which 
ho  used  cost  him  in  the  end? 

23.  Bought    6    quarts   of  berries,  at   8   cents  a  quart ; 
sold  4  quarts,   at    10  cents  a  quart,  and    2    quarts,  at  12 
cents  a  quart :    how  much  did  I  make  ? 


M  ULTIPLICATION.  35 

24.  If  an  orange  cost    5   cents,  and   an  apple  2  cents, 
what  will  2  oranges  and  4  apples  cost? 

25.  If  pork  is  8  cents,  and  beef  10  cents  a  pound,  what 
will  7  pounds  of  pork  and  6  pounds  of  beef  cost? 

26.  If  an   orange  cost   5   times   as  much   as  an  apple, 
how  much   more  will  6  oranges    cost   than  25  apples,  if 
an  apple  is  worth  1  cent? 

27.  Bought,  at  one  time,  5  yards  of  muslin,  at  10  cents 
a  yard;    at    another,  10    yards,  at  5  cents  a  yard:    how 
much  did  it  all  cost? 

28.  If  a  man  earn  $15  per  week,  and  spend  $11  a  week, 
how  much  will  he  save  in  3  weeks?     How  much  can  he 
save  in  8  weeks? 

29.  A  miller  bought  10  bushels  of  wheat,   at    1   dollar 
a  bushel,   from    which  he  made    2    barrels  of  flour   that 
were  sold  at  7  dollars  each :  how  much  more  did  he  get 
for  the  flour  than  he  paid  for  the  wheat? 

30.  Thomas    has   8    books,    and    his   brother    has    five 
times  as  many  less  6 :  how  many  books  have  both  ? 

31.  What    will    9    pounds    of  tigs   cost,   at  12  cents  a 
pound  ? 

32.  A  man   employed   one   laborer   for   6   weeks,  at  7 
dollars  a  week,  and   another   for   5   days,  at   2  dollars  a 
day:  how  much  did  he  have  to  pay  both? 

33.  A  farmer  sold    5  dozen  eggs,  at  11    cents  a  dozen, 
and   bought   3  pounds   of  sugar,    at   12   cents  a  pound: 
how  many  cents  were  due  him? 

34.  Seven  times  9  are  how  many? 

35.  How  many  are  2  times  3  times  4? 

36.  How  many  are  4  times  3  times  12? 

37.  A  man    bought  a  calf  for  11  dollars    and  paid  six 
times   as    much   for   a    cow :     how  much    did   both    cost, 
him? 

38.  Give  the  product  of  8  multiplied  by  8? 


LESSON  XVI. 


1.  At  1  cent  each,  how  many  cakes  can  you  buy  for  4 
cents?     Ans.  4  cakes. 

Why?     Ans.  Because  1  is  contained  in  4,  four  times. 

2.  At  2  cents  each,  how  many  apples  can  you  buy  for  4 
cents  ? 

3.  Among  how  many  boys   can   6   apples  be   divided, 
giving  to  each  boy  2  apples? 

4.  At  2  cents  each,  how  many  apples  can  you  buy  for  8 
cents  ? 

5.  At  3  cents  each,  how  many  peaches  can  you  buy  for 
6  cents? 

6.  At  3  cents  each,  how  many  pears  can  you  buy  for  9 
cents  ? 

7.  At  2  cents  each,  how  many  cakes  can  you  buy  for  10 
cents? 

8.  At  2   cents    each,  how  many  balls   can  you   buy  for 

14  cents? 

9.  At  5  cents  each,  how  many  lemons  can  you  buy  for 

15  cents? 

10.  A  boy  has  16  marbles,  and  wishes  to  divide  them 
into  piles  of  2  each:  how  many  piles  must  there  be? 

11.  At  3  cents  each,  how  many  plums  can  you  buy  for 
18  cents? 

12.  At  5  cents  each,  how  many  oranges  can  you  buy  for 
20  cents? 


13.  At  $3  a  yard,  how  many  yards  of  cloth  can 
buy  for  $21  ? 

14.  A  lady  spent  22  cents  for  tape  at  2  cents  a  yard : 
how  many  yards  did  she  buy  ? 

15.  At  6  cents  each,  how  many  oranges  can  you  buy  for 
24  cents  ?    How  many  at  8  cents  each  ? 

16.  In  an  orchard  of  25  apple  trees  there  are  5  rows: 
how  many  trees  in  each  row  ? 

17.  If  a  man  can  travel  3  miles  in  an  hour,  how  many 
hours  will  it  take  him  to  travel  27  miles  ? 

18.  A  man  gave  $28  for  sheep,  at  $4  a  head :  how  many 
did  he  buy? 

19.  If  you  had  30  cents,  how  many  marbles  could  you 
buy  at  3  cents  each  ? 

20.  There  are  32  dimes  on  a  table  in  4  piles :  how  many 
in  each  pile? 

21.  In  an  orchard  containing  35  apple  trees,  there  are  5 
rows :  how  many  trees  are  there  in  each  row  ? 

22.  Six  men  receive  $36  for  a  job  of  work :  what  is  each 
man's  share? 

23.  Four  quarts  make  1  gallon :  how  many  gallons  in 
36  quarts? 

24.  If  a  man  travel  10  miles  in  1  hour,  in  how  many 
hours  will  he  travel  40  miles? 

25.  Forty-two    cents    were    divided    equally    among    6 
boys :  how  many  cents  did  each  boy  receive  ? 

26.  If  you    divide  45  oranges    equally  among  9  boys: 
how  many  oranges  will  each  boy  receive? 

Division  is  the  process  of  finding  how  many  times  one 
number  is  contained  in  another. 

The  divisor  is  the  number  by  which  to  divide.  The 
dividend  is  the  number  to  be  divided.  The  quotient  is  the 
result.  The  sign  of  division  (-j-)  is  read  divided  by. 


38        RAY'S    NEW   INTELLECTUAL  ARITHMETIC. 


LESSON   XVII. 
DIVISION   TABLE. 


2- 

9      1 

—  £  =   1 

3- 

o     -i 
—  o  =  1 

4- 

-4  =  1 

4- 

-2^   2 

6- 

-3=  2 

8- 

-4=  2 

6- 

-2=  3 

9- 

-3=  3 

12- 

-4=  3 

8- 

-2=  4 

12- 

-3=  4 

16- 

-4=  4 

10- 

-2=  5 

15- 

-3=  5 

20- 

-4=  5 

12- 

-2=  6 

18- 

-3=  6 

24- 

-4=  6 

14- 

-2=  7 

21- 

-3=  7 

28- 

-4=  7 

16- 

-2=  8 

24- 

-3=  8 

32- 

-4=  8 

18- 

-2=  9 

27- 

-3=  9 

36- 

-4=  9 

20- 

-2  =  10 

30- 

-3  =  10 

40- 

-4  =  10 

22- 

-2  =  11 

33- 

-3  =  11 

44- 

-4  =  11 

24- 

-2  =  12 

36- 

-3  =  12 

48- 

-4  =  12 

5- 

-5=  1 

6- 

-6=  1 

7- 

-7=  1 

10- 

-5=  2 

12- 

-6=  2 

14- 

-7=  2 

15- 

-5=  3 

18- 

-6=  3 

21- 

-7=  3 

20- 

-5=  4 

24- 

-6=  4 

28- 

-7=  4 

25- 

-5=  5 

30- 

-6=  5 

35- 

-7=  5 

30- 

-5=  6 

36- 

-6=  6 

42- 

-7=  6 

35- 

-5=  7 

42- 

-6=  7 

A.^  - 

-7=  7 

40- 

-5=  8 

48- 

-6=  8 

56- 

-7=  8 

45- 

-5=  9 

54- 

-6=  9 

63- 

-7=  9 

50- 

-5  =  10 

60- 

-6  =  10 

70- 

-7  =  10 

55- 

-5  =  11 

66- 

-6  =  11 

77- 

-7  =  11 

60- 

-5  =  12 

72- 

-6  =  12 

84- 

-7  =  12 

DIVISION. 


39 


8- 

-8=    1 

9- 

-9=    1 

10- 

-10=    1 

16- 

-8=    2 

18- 

-9=    2 

20- 

-10=    2 

24- 

-8=   3 

27- 

-9=    3 

30- 

-10=    3 

32- 

-8=    4 

36- 

-9=    4 

40- 

-10=    4 

40- 

-8=    5 

45- 

-9=    5 

50- 

-10=    5 

48- 

8f> 
O 

54- 

-9=    6 

60- 

-10=    6 

56- 

-8=   7 

63- 

-9=7 

70- 

-10=   7 

64- 

-8=    8 

72- 

-9=    8 

80- 

-10=    8 

72- 

-8=    9 

81- 

-9=    9 

90- 

-10=    9 

80- 

-8  =  10 

90- 

-9  =  10 

100- 

-10  =  10 

88- 

-8  =  11 

99- 

-9  =  11 

110- 

-10  =  11 

96- 

-8  =  12 

108- 

-9  =  12 

120- 

-10  =  12 

11- 

-11=    1 

12- 

-12=    1 

22- 

-11=    2 

24- 

-12=    2 

33- 

-11=    3 

36- 

-12=    3 

44- 

-11=    4 

48- 

-12=    4 

55- 

-11=    5 

60- 

-12=    5 

66- 

-11=    6 

72- 

-12=    6 

77- 

-11=    7 

84- 

-12=    7 

oo  — 

-11=    8 

96- 

-12=    8 

99- 

-11=    9 

108- 

-12=    9 

110- 

-11  =  10 

120- 

-12  =  10 

121- 

-11  =  11 

132- 

-12  =  11 

132- 

-11  =  12 

144- 

-12  =  12 

40       KAY'S    NEW  INTELLECTUAL  ARITHMETIC. 

LESSON  XVIII. 

1.  Two  is  contained  in  12  how  many  times? 
SOLUTION. — 2  is  contained  in  12  six  times. 

2.  Two  in  16  how  many  times?    2  in  24?    3  in  9?    Sin 
15?     3  in  21?     3  in  27?     4  in  8?     4  in  20?     4  in  28? 

4  in  36?     4  in  48? 

3.  Five  is  contained  in  15  how  many  times?     5  in  30? 

5  in  45?     5  in  60?     6  in  18?     6  in  24?     6  in  36?     6  in 
42?     6  in  54?     6  in  66? 

4.  Seven  in  14  how  many  times?     7  in  28?     7  in  42? 
7  in  56?     7  in  63?     7  in  84?     8  in  24?     8  in  40?     8  in 
56?     8  in  72?     8  in  96? 

5.  Nine  in  18  how  many  times?      9  in  27?     9  in  45? 
9  in  54?     9  in  63?     9  in  81  ?     9  in  108?     10  in  20?     10 
in  60?     10  in  90?     10  in  100? 

6.  Eleven   in  55  how  many  times?     11   in  77?     11  in 
99?     11  in  110?     11  in  121?     12  in  24?     12  in  48?     12 
in  60?     12    in    72?     12   in  96?     12  in  108?     12  in  120? 
12  in  144? 

7.  If  12  peaches  be  divided  equally  among  3  children, 
how  many  will  each  child  have? 

SOLUTION. — Each  child  will  have  one-third  of  12  peaches,  which 
is  4  peaches, 

8.  Four  boys  gave  their  sister  24  apples,  each  an  equal 
number :  how  many  did  each  give  ? 

9.  A  mother  divided    20    cents   equally  between  her  2 
little  girls:  how  many  did  each  receive? 

10.  Five  books  cost  35  cents:  how  much  is  that  apiece? 

11.  A  man  has  $40 :  if  he  spend  $5  a  week,  how  long 
will  it  last? 

SOLUTION. — The  money  will  last  as  many  weeks  as  $5  are  con- 
tained times  in  $40,  which  are  8. 


DIVISION.  41 

12.  If  5  apples  arc  worth  1  pear,  how  many  pears  are 
25  apples  worth?     35  apples?     45  apples? 

13.  If  6  pears  are  worth  an  orange,  how  many  oranges 
can  you  get  for  30  pears?     For  42  pears?     For  54  pears? 
For  66  pears? 

14.  If  1  man  do  a  piece  of  work  in  42  days,  how  many 
days  will  it  take  7  men  to  perform  it? 

15.  If  1  man  can  eat  a  certain  quantity  of  provisions 
in  56  days,  how  many  days  will  it  last  7  men? 

16.  If  1  pipe  empty  a  cistern  in  63  hours,  in  how  many 
hours  will  9  pipes  of  the  same  size  empty  it? 

17.  If  hay  is  worth  $9    a  ton,   how  many  tons  can  be 
bought  for  $27?     For  $45?     For  $54?     For  $63? 

18.  Ten  men   bought  a  horse  for  $60 :    how  much  did 
each  one  pay? 

19.  If  11  ounces  of  powder  cost  88  cents:  what  will  1 
ounce  cost? 

20.  A  man  paid  $108  for  12  merino  sheep :  how  much 
was  that  apiece? 

21.  In  an  orchard  there  are  120  trees  in  10  rows :  how 
many  trees  in  each  row? 

22.  A  man  earns  $144  in  12  weeks :  how  much  is  that 
a  week?     How  much  a  day,  allowing  6  working  days  to 
the  week? 

23.  If  6  men  earn  $84  in  7  days,  how  much  does  each 
man  earn  in  1  day? 

SOLUTION. — In  one  day  they  earn  one-seventh  of  $84,  which  is  $12; 
then,  each  man  earns  in  one  day  one-sixth  of  $12,  which  is  $2. 

24.  If  9  men    earn  $108  in  3  days,  how  much  does  1 
man  earn  ?     How  much  does  each  man  earn  in  1  day  ? 

25.  One  man  travels  at  the  rate  of  15  miles  in  3  days; 
another  at  the  rate  of  20  miles  in    2    days:    how   much 
further  in  one  day  docs  the  latter  travel  than  the  former  ? 


42        KAY'S    NEW   INTELLECTUAL  AKITHMETIC. 


LESSON   XIX. 

1.  Twelve  is  how  many  times  2? 

SOLUTION. — As  many  as  2  is  contained  times  in  12,  which  arc  6. 

2.  Twenty-four  is  how  many  times  3?     6?    8?     12? 

3.  Seventy -two  is  how  many  times  12?     8?     6?     9? 

4.  How  many  oranges,  at  5  cents  each,  must  be  given 
for  10  pears,  at  2  cents  each? 

SOLUTION. — The  pears  cost  10  times  2  cents,  which  are  20  cents; 
for  this,  as  many  oranges  must  be  given  as  5  cents  are  contained  times 
in  20  cents,  which  are  4. 

5.  A   wheel   is   10   feet   in    circumference:    how  many 
revolutions  will  it  make  in  going  120  feet? 

6.  An  orchard  contains  10  rows  of  trees,  and  6  trees  in 
a  row ;  if  there  were  but  5  rows,  how  many  trees  would 
there  be  in  a  row? 

7.  I    have   three   times    as   many  marbles   as  the  sum 
of   1,    2,  arid    3,  is    contained    times    in    60:    how    many 
have  I? 

SOLUTION. — 1  and  2  and  3  are  6;  6  is  contained  in  60,  10  times; 
8  times  10  are  30. 

8.  Bought  6  hats,  at   $5  apiece,  and  4  yards  of  cloth, 
at  $3  a  yard;    gave   in    exchange   flour,   at  $6  a  barrel: 
how  many  barrels  did  it  take? 

SOLUTION. — The  hats  cost  6  times  $5,  which  are  $30;  the  cloth,  4 
times  $3,  which  are  $12;  both  cost  $30  plus  $12,  which  are  $42.  It 
took  as  many  barrels  as  $6  are  contained  times  in  $42,  which  are  7. 

9.  If  a  man  gain  6   miles  in   5  hours,  how  long  will  it 
take  to  gain  24  miles? 

SOLUTION. — 24  miles  are  4  times  6  miles;  then,  it  will  take  4  times 
5  hours,  which  are  20  hours. 


DIVISION.  43 

10.  Two  times  6  arc  contained  how  many  times  in  the 
sum  of  36  arid  12? 

11.  If  60  be   divided  by  some  number,   the  result  will 
be  10:  what  is  that  number? 

12.  I  have  a  number  in  my  mind  which,  divided  by  3, 
gives  2  times  6 :  what  is  the  number  ? 

13.  If  I  purchase  lemons  at  the  rate  of  2  for  6  cents, 
and  sell  7  for  28  cents,  how  much  do  I  gain? 

14.  A  man  has  a  job  of  work  which  9  men  can  per- 
form in  2  days ;  he  desires  to  complete  it  in  3  days :  how 
many  men  must  he  employ? 

15.  Five  times  the  sum  of  two  numbers  is  equal  to  60  ; 
if  7  is  one  of  them,  what  is  the  other? 

16.  Henry  has  6  dimes;  Thomas, twice  as  many  less  2; 
and  Samuel, 3  times  as  many  as  Henry:  how  many  have 
they  together? 

17.  If  to    the    number   of  times  4    is  contained  in  12, 
you   add    3,  and   subtract   the   result   from    9,  what  will 
remain  ? 

18.  Five  oranges  were  sold   for  25  cents,  and  10  centa 
were  gained:  what  did  each  cost? 

19.  What  number  subtracted  from  17,  will  leave  double 
the  remainder  that  5  from  9  leaves? 

20.  A  boy  said  that  10  taken  from  the  number  of  apples 
he  had,  left  twice  as  great  a  remainder  as  the  difference 
between  12  and  8:  how  many  had  he? 

21.  If  you  multiply  any  number,  10,  by  any  other  num- 
ber, 5,  and  divide  the  product  by  the  same  number,  5, 
what  will  be  the  result  ? 

22.  If  2  oranges  are  worth  5  apples,  how  many  apples 
are  12  oranges  worth? 

SOLUTION. — 12  oranges  are  6  times  2  oranges;  then,  they  are  worth 
6  times  5  apples,  which  are  30  apples. 


44        KAY'S    NEW    INTELLECTUAL   ARITHMETIC. 

23.  One  man  goes  10  miles  while  another  goes  7 ;  when 
the  first  has  gone  90  miles,  how  far  has  the  second  gone? 

24.  James  earns   8   cents  while  John   earns   12;  when 
John  has  earned  60,  how  many  has  James  earned? 

25.  George   recites   5   lessons  while    Charles  recites  4; 
how  many  lessons  have  both  recited  when   Charles  has 
recited  20? 

26.  A  man  earns  $9  while  a  boy  earns  $5:  how  many 
dollars  have  both  earned  when  the  man  has  earned  $36? 

27.  A  certain    number  multiplied   by  10  is  5  less  than 
45 :  what  is  that  number  ? 

28.  How  many  barrels  of  flour,  at   $9  a   barrel,  could 
you  buy  for  $54? 

2'9.  William  counts  11  while  James  counts  7  :  how  many 
does  James  count  while  William  is  counting  77  ? 

30.  How  many   yards   of  velvet,   at   $12   a  yard,  can 
be  obtained  for  $108? 

31.  If  8  sheep  cost  $56,  how  much  will  3  sheep  cost? 

32.  At  4  cents  a  pound,  how  many  pounds  of  salt  can 
you  buy  with  44  cents? 

33.  If  a  man  travel  at  the   rate  of  10  miles  an  hour, 
how  long  will  it  take  him  to  go  100  miles? 

34.  How  many  men  can  in  5  days  do  a  piece  of  work 
which  occupies  3  men  10  days? 

35.  How  many  men  can  in  3  days  do  the  same  amount 
of  work  that  employs  9  men  4  days? 


LESSON    XX. 

A  unit  is  a  single  thing ;  as,  one  apple. 
If  a  unit  is  divided  into  two  equal  parts,  one  of  the 
parts  is  called  ONE-HALF. 

1.  How  many  halves   in  2  apples?     In  3?     In  4?     In 
5?     In  6?     In  7?     In  8?     In  9?     In  10? 

SOLUTION. — In  1  apple  there  are  2  halves,  and  in  2  apples  there 
are  2  times  2  halves,  which  are  4  halves. 

If  a  unit  is  divided  into  three  equal  parts,  each  part 
is  called  ONE-THIRD  ;  two  parts  are  called  TWO-THIRDS  ;  and 
three  parts,  THREE-THIRDS,  or  the  whole. 

2.  How  many  thirds  in  2  apples  ?     In  3  ?     In  4  ?     In  5  ? 
In  6?     In  7?     In  8?     In  9?     In  10? 

If  a  unit  is  divided  into  four  equal  parts,  each  part  is 
called  ONE-FOURTH;  two  parts  are  called  TWO-FOURTHS; 
three  parts,  THREE-FOURTHS  ;  and  four  parts,  FOUR-FOURTHS, 
or  the  whole. 

3.  How  many  fourths  in  2  apples?     In  3?     In  4?     In 
5?     In  6?     In'??     In  8?     In  9?     In  10? 

If  a  unit  is  divided  into  5  equal  parts,  each  part  is 
called  ONE-FIFTH  ;  2  parts  are  called  TWO-FIFTHS  ;  3  parts, 
THREE-FIFTHS;  4  parts,  FOUR-FIFTHS;  and  5  parts,  FIVE- 
FIFTHS,  or  the  whole. 

4    How  many  fifths  in  2  apples?     In  3?     In  4?     In  5? 

In  6?     In  7?     In  8?     In  9?     In  10? 

(45) 


46        RAY'S    NEW   INTELLECTUAL  ARITHMETIC. 

If  a  unit  is  divided  into  6  equal  parts,  each  part  is 
called  ONE-SIXTH  ;  2  parts  are  called  TWO-SIXTHS  ;  3  parts, 

THREE-SIXTHS  ;    4  parts,  FOUR-SIXTHS  J    5  parts,  FIVE-SIXTHS  ; 

and  6  parts,  SIX-SIXTHS,  or  the  whole. 

5.  How  many  sixths  in  2  apples?     In  3?     In  4?     In  5? 
In  6?     In  7?     In  8?     In  9?     In  10? 

If  a  unit  is  divided  into  7  equal  parts,  each  part  is 
called  ONE-SEVENTH  ;  2  parts  are  called  TWO-SEVENTHS  ; 
3  parts,  THREE-SEVENTHS;  4  parts,  FOUR-SEVENTHS;  5 
parts,  FIVE-SEVENTHS;  6  parts,  SIX-SEVENTHS;  and  7  parts, 
SEVEN-SEVENTHS,  or  the  whole. 

6.  How  many  sevenths  in  2  apples  ?     In  3  ?     In  4  ?     In 
5?     In  6?     In  7?     In  8?     In  9?     In  10? 

If  a  unit  is  divided  into  8  equal  parts,  each  part  is 
called  ONE-EIGHTH;  2  parts  are  called  TWO-EIGHTHS;  3 
parts,  THREE-EIGHTHS;  4  parts,  FOUR-EIGHTHS;  5  parts, 
FIVE-EIGHTHS;  6  parts,  SIX-EIGHTHS;  7  parts,  SEVEN- 
EIGHTHS;  and  8  parts,  EIGHT-EIGHTHS,  or  the  whole. 

7.  How  many  eighths  in  2  apples?     In  3?     In  4?     In 
5?     In  6?     In  7?     In  8?     In  9?     In  10? 

If  a  unit  is  divided  into  9  equal  parts,  each  part  is 
called  ONE-NINTH;  2  parts  are  called  TWO-NINTHS;  3  parts, 
THREE-NINTHS;  4  parts,  FOUR-NINTHS;  5  parts,  FIVE-NINTHS; 
6  parts,  SIX-NINTHS;  7  parts,  SEVEN-NINTHS;  8  parts,  EIGHT- 
NINTHS  ;  and  9  parts,  NINE-NINTHS,  or  the  whole. 

8.  How  many  ninths  in   2  apples?     In  3?     In  4?     In 
5?     In  6?     In  7?     In  8?     In  9?     In  10? 

9.  How   many  thirds   in    3  units?     How  many  fifths? 
Sevenths?     Ninths? 

10.  How   many   fourths    in    5    oranges?      How    many 
eighths?     Thirds? 

11.  In  11    apples,    how    many    sixths?      How    many 
halves?     Fifths?    Ninths? 


FRACTIONS.  47 

LESSON  XXL 

A  fraction  is  one  or  more  equal  parts  of  a  unit. 

A  fraction  is  represented  by  writing  two  numbers,  one 
above  the  other,  with  a  line  between  them.  Thus,  one- 
half  is  written  J;  two-fifths  are  written  f ;  five-sevenths, 
£,  etc. 

The  lower  number  shows  the  number  of  parts  into 
which  the  unit  is  divided ;  it  is  called  the  denominator. 

The  upper  number  shows  how  many  parts  of  the  unit 
are  taken ;  it  is  called  the  numerator. 

The  numerator  and  denominator  are  styled  the  terms 
of  the  fraction. 

Write  the  following  fractions: 

Two-thirds,  four-fifths,  six-sevenths,  eight-ninths,  one- 
tenth,  three-tenths,  nine-tenths,  seven-elevenths,  five 
twelfths,  seven-thirteenths,  nine-fourteenths,  thirteen-fif- 
teenths,  one-sixteenth,  two-seventeenths,  five-eighteenths, 
six-nineteenths,  seventeen-twentieths,  twenty-seven  thirty- 
firsts,  thirty-four  forty-thirds,  twenty-nine  fifty-sixths, 
forty-two  sixty-sevenths,  fifty-seven  seventy-firsts,  sixty- 
nine  eighty-seconds,  seventy-one  ninety-eighths,  eighty- 
five  one-hundred-and-twenty-thirds. 

Eead  the  following  fractions: 

*.    ».    I.    A,   tV  H,    tt,    If,   *f 

In  the  fraction  f,  the  number  of  parts,  two,  which  are 
taken,  is  less  than  the  number  of  parts,  three,  into  which 
the  unit  is  divided;  hence,  the  value  of  the  fraction  is 
less  than  1.  In  the  fraction  J,  the  number  of  parts  taken 
equals  the  number  of  parts  into  which  the  unit  is  divided ; 


48        RAY'S    NEW   INTELLECTUAL   ARITHMETIC. 

hence  the  value  of  the  fraction  is  equal  to  1.  In  the 
fraction  f,  the  number  of  parts  taken  is  greater  than  the 
number  of  parts  into  which  a  single  unit  is  divided,  and 
hence  the  value  of  the  fraction  is  greater  than  1. 

A  proper  fraction  is  one  whose  value  is  less  than  1. 

An  improper  fraction  is  one  whose  value  is  equal  to  or 
greater  than  1. 

Point  out  the  proper  and  improper  fractions  in  the 
following  examples  : 

i,   f    I-    *.    f    *.    i>    f    A>    ¥> 

TT»      T£>       T¥>        T¥>      IT'      ff>      TF>      7T' 

A  mixed  number  is  composed  of  a  whole  number  and 
a  fraction.  Thus,  2J,  3|f  5^;  read,  two  and  one-half, 
three  and  one-third,  five  and  two-sevenths. 

Head  the  following  examples: 


LESSON  XXII. 

1.  If  a  yard  of  tape  is  worth  2  cents,  what  is  J  of  a 
yard  worth? 

SOLUTION.  —  £  of  a  yard  is  worth  $  of  2  cents,  which  is  1  cent. 

2.  If  an  apple   is  worth  3  cents,  what  is  J  of  the  ap- 
ple worth? 

3.  A  yard  of  cloth  costs  $6,  what  would   §  of  a  yard 
cost? 

SOLUTION.—  J  of  a  yard  would  cost  £  of  $6,  which  is  $2;  then,  § 
of  a  yard  would  cost  2  times  $2,  which  are  $4. 


FRACTIONS.  49 

4.  James  had  4  apples  and  gave  his  brother  £  of  them : 
how  many  did  he  give  him? 

5.  If  a  melon  is  worth  8  cents,  what  are  f  of  a  melon 
worth  ? 

6.  If  a  barrel  of  flour  costs  $10,  what  is  the  cost  of  | 
of  a  barrel?     Off?     Off? 

7.  If  a  dozen  eggs  are  worth  12  cents,  what  arc  f  of  a 
dozen  worth? 

8.  What  are  f  of  9  ? 

SOLUTION. — J  of  9  is  3;  then,  f  of  9  are  2  times  3,  which  are  6. 

9.  What  are  f  of  20? 

10.  What  are  f  of  15?    f  of  20?    f  of  25? 

11.  What  are  f  of  14?     |  of  21?     $  of  28?     f  of  35? 
f  of  42  ? 

12.  What  are  f  of  16?    f  of  24?     J  of  32? 

13.  What  are  I  of    9?    |  of  18?    f  of  27?    %  of  36? 
|  of  45? 

14.  What  are  ft  of  10?     -^  of  20?    ^  of  30? 

15.  What  are  ft  of  11?    ^r  of  22?     T4T  of  33?    -fy  of 
44?    JL.0f55?    ^of66?    ^-of77? 

16.  What  are  ^  of  24?    -^  of  36?.   |J  of  48? 

17.  If  2  apples  cost  4  cents,  what  will  1  apple  cost? 

SOLUTION. — 1  apple  will  cost  £  of  4  cents,  which  is  2  cents. 

18.  If  3  yards  of  cloth  cost  $9,  what  will  1  yard  cost? 

19.  If  3  oranges  are  worth  15  cents,  what  are  2  oranges 
worth  ? 

SOLUTION. — 1  orange  is  worth  £  of  15,  or 5,  cents;  then,  2  oranges 
are  worth  2  times  5  cents,  which  are  10  cents. 

20.  If  5  barrels  of  flour  are  sold  for  $30,  what  would  3 
barrels  sell  for? 

-  int.  4. 


50         KAY'S  NEW  INTELLECTUAL  ARITHMETIC. 

21.  A  grocer  sells  7  pounds  of  sugar  for  70  cents  :  what 
will  he  sell  5  pounds  for? 

22.  A  lady  purchased   8  yards  of  calico  for  72  cents; 
she  afterward  found  that  she  needed  5  yards  more  of  the 
same:  how  much  did  it  cost? 

23.  A  drover  bought  12  calves  for  $120;   he  sold  7  of 
them  for  what  they  cost  him  :  what  did  he  get  for  them  ? 


LESSON   XXIII. 


1.  If  an  apple  costs  2  cents,  what  part  of  the  apple  costs 
1  cent? 

SOLUTION. — 1  cent  is  the  cost  of  £  of  the  apple. 

2.  A  boy  bought  a  pear  for  3  cents :  what  part  of  the 
pear  cost  1  cent? 

3.  If  the  price  of  a  yard  of  cloth  is  $3,  what  part  of  a 
yard  will  cost  $2  ? 

SOLUTION. — $1  will  be  the  cost  of  £  of  a  yard;  then  $2  will  be  the 
cost  of  2  times  £  of  a  yard,  which  are  f  of  a  yard. 

4.  If  you  buy  an  orange  for  4  cents,  what  part  of  the 
orange  costs  3  cents? 

5.  If  a  melon  is  worth  5  cents,  what  part  of  the  melon 
is  worth  2  cents  ?     3  cents  ?     4  cents  ? 

6.  If  a  barrel  of  apples  cost  $6,  what  part  of  a  barrel 
will  cost  $5? 

7.  James  had    7   marbles  and   gave   his   brother  4  of 
them :  what  part  did  he  give  away  ? 

8.  A  lady  went  shopping  with  $10 ;  she  spent  $7 :  what 
part  of  her  money  did  she  spend  ? 


FHACTIONS.  51 

9.  If  a  bushel  of  clover  seed   cost  $8,  what  part  of  a 
bushel  can  be  bought  for  $5  ? 

10.  5  is  what  part  of  7? 

SOLUTION. — 1  is  \  of  7;  then,  5  is  5  times  $=  f  of  7. 

11.  Sis  what  part  of  8?     Of  10?     Of  11?     Of  20? 

12.  4  is  what  part  of  9?     Of  11?     Of  15?     Of  25? 

13.  5  is  what  part  of  8?     Of  9?     Of  12?     Of  16? 

14.  What  part  of  15  is  2?     7?     8?     11?     13? 

15.  What  part  of  20  is  3?     7?     11?     13?     17? 

16.  f  of  30  is  what  part  of  23? 

17.  £  of  28  is  what  part  of  35? 

18.  |  of  21  is  what  part  of  19? 

19.  ^  of  4  is  what  part  of  |  of  9?  ^^, 

20.  |  of  12  is  what  part  of  £  of  24. 

21.  f  of  10  is  what  part  of  f  of  21? 

22.  |  of  16  is  what  part  of  %  of  35? 

23.  |  of  18  is  what  part  of  ^-  of  77? 

24.  ^  of  30  is  what  part  of  f-  of  49  ? 


LESSON    XXIV. 

1.  If  -J-   an  apple   is  worth   1  cent,   what   is  the   apple 
worth  ? 

SOLUTION. — The  apple  is  worth  2  times  1  cent  =  2  cents. 

2.  If  ^  of  an    orange    is    worth    2    cents,  what  is  the 
orange  worth? 

3.  If  %  of  a  lemon  are  worth  6  cents,  what  is  the  lemon 
worth  ? 

SOLUTION. — £  of  the  lemon  is  worth  f  of  6  cents  =  3  cents;  then, 
the  lemon  is  worth  3  times  3  cents  =  9  cents. 


52        KAY'S    NEW   INTELLECTUAL  ARITHMETIC. 

4.  If  |  of  a  barrel  of  flour  cost  $9,  what  will  a  barrel 
cost? 

5.  If  |  of  a  pound  of  coffee  cost  10  cents,  what  is  the 
price  of  a  pound? 

6.  If  |  of  a  pound  of  butter  cost    12   cents,  what  will 
a  pound  cost? 

7.  If  |  of  a  gallon  of  wine  cost  35  cents,  what  will  a 
gallon  cost? 

8.  6  is  %  of  what  number? 

SOLUTION. — \  of  the  number  is  £  of  6  =  3;  then,  the  number  is 
7  times  3  =  21. 

9.  6  is  |  of  what  number  ?    T2T  ? 

10.  12  is  f  of  what  number?     f?     f?     f?    -\? 

11.  20  is  $•  of  what  number?     ^?     f?     T4T? 

12.  30  is  -f  of  what  number?     f?     f?     |?     T5T? 

13.  42  is  £  of  what  number?     T6T? 

14.  56  is  I  of  what  number?     J?     T^? 

15.  72  is  f  of  what  number?     T8r? 

16.  90  is  T%  of  what  number? 

17.  If  you  have  8  cents,  and  f  of  your  money  equals 
J  of  mine,  how  many  cents  have  I  ? 

SOLUTION. — |  of  8  cents  =  6  cents;  then,  if  f  of  my  money  =  6 
cents,  ^  of  my  money  is  |  of  6  cents  =  3  cents,  and  all  my  money  is 
3  times  3  cents  =  9  cents. 

18.  William   says   to    Frank:    "Your   age   is  15  years, 
and  £  of  your  age  is  J  of  mine:  what  is  my  age?" 

19.  f-  of  18  are  f  of  what  number? 

SOLUTION.— f  of  18  =  15;  then,  f  of  some  number  =  15.  \  of  the 
number  is  |  of  15  =  5,  and  the  number  is  5  times  5  =  25. 

20.  %  of  14  are  f  of  what  number  ? 

21.  of  16  are      of  what  number? 


FRACTIONS.  53 


22.  |     of  27  are  ^  of  what  number? 

23.  |-    of  36  are  T\  of  what  number  ? 

24.  ^  of  20  are  T2T  of  what  number  ? 
25          of  55  are  -      of  what  number? 


LESSON  XXV. 

1.  Divide  3  apples  between  2  boys,  giving  to  each  the 
same  amount. 

SOLUTION.  —  Each  boy  will  receive  £  of  3  apples,  which  is  f  =  1  1 
apples. 

2.  A  grocer  gave  4   oranges  to  3  boys,  provided  they 
would  divide  them  equally  :  what  was  the  share  of  each  ? 

3.  If  2  pears  cost  5  cents,  how  much  is  that  apiece? 

4.  If  3  yards  of  cloth  cost  $5,  what   is   the  price  per 
yard? 

5.  Henry  bought   4   pens   for  5   cents:    what  was  the 
cost  of  each  ? 

6.  %  of  6  =  what? 
SOLUTION.—  |  of  6  is  f  =  1  £. 

7.  £  of    7  =  what?    J  of  7?    |of7?    iof7?    £of7? 

8.  4  of    8  =  what?    |  of  8?    |of8? 

9.  %  of    9  =  what?    £of9?    |of9?    |of9?    |of9? 

10.  £  of  10  =  what?     I  of  10?    JoflO? 

11.  i  of  11=  what?     4  of  11?     Jofll?     £  of  11?    i 
of  11?    |  of  11?    |  of  11?    £ofll?    TVofll? 

12.  £  of  12  =  what?    |  of  12?    JL  of  12? 

13.  For   5   cents,    how   many   apples   can   I   buy  at   2 
cents  each? 

SOLUTION.—  I  can  buy  as  many  apples  as  2  cents  are  contained  times 
in  5  cents,  which  are  f  =  2|. 


54         KAY'S  NEW  INTELLECTUAL  ARITHMETIC. 

14.  At   $3   a   yard,  how  many  yards    of  cloth  can  be 
purchased  for  $7? 

15.  Harriet  spent  13  cents  for  braid,  at  4  cents  a  yard, 
how  many  yards  did  she  buy? 

16.  When    milk    is    worth    5    cents  a  pint,  how  many 
pints  can  you  get  for  17  cents?  IS1 

17.  For   $23,  how  much   flour    can   be  bought  at  $6  a 
barrel? 

18.  A  lady  spent  25  cents  for  ribbon,  at  7  cents  a  yard, 
how  many  yards  did  she  buy  ? 

19.  How  many  times     2  is  13? 

SOLUTION. — As  many  as  2  is  contained  times  in  13,  which  are  ^ 


20. 
21. 
22. 
23. 
24. 
25. 
26. 
27. 
28. 

How 
How 
How 
How 
How 
How 
How 
How 
How 

many 
many 
many 
many 
many 
many 
many 
many 
many 

times 
times 
times 
times 
times 
times 
times 
times 
times 

2 

3 
4 
6 

7 
8 
9 
10 
11 

is 
is 
is 
is 
is 
is 
is 
is 
is 

15? 
20? 
27? 
43? 
24? 
45? 
34? 
63? 
42? 

17? 
26? 
33? 
47?' 
32? 
55? 
38?- 
69? 
46? 

19? 
29? 
39? 
49? 
40? 
67? 
50? 
77? 
54? 

21? 
31? 
41? 
59? 

48? 
71? 
58? 
83? 
60? 

23? 
35? 

47? 
61? 
57? 
81? 
64? 
91? 
70? 

29.  How  many  times  12  is  68?     79?     85?    89?     95? 


LESSON  XXVL 


1.  How  many  halves  in 

SOLUTION.—  In  1  there  are  f;  then,  in  2  there  are  2  times  f  —  f; 


2.  How  many  halves  in  3J?     4J?     5£?     6|? 

3.  How  many  thirds  in  4J?     5f  ?     6£?     7f  ? 


FKACTIONS.  55 

4.  How  many  fourths  in  3£?     4J?     5J?     6}? 

5.  How  many  fifths  in  1£?     3|?     6|?     7£?     t,- 

6.  How  many  sixths  in  2f  ?    4|?     5J-?     6f  ? 

7.  How  many  sevenths  in  5f  ?     6£?     7-f  ?     8f  ? 

8.  How  many  eighths  in  3|?     4J?     5|?     6f? 

9.  How  many  ninths  in  6f  ?     7J-?     8f?     9|? 

10.  How  many  tenths  in  6T%?     7^?     8^?     9TV? 

11.  How  many  elevenths  in  6^?     7^-?     8^?     9^-? 

12.  How  many  twelfths  in  5T^?     6^?     7^?     9^? 

u 


LESSON   XXVII. 

NOTE. — A  fraction  is  in  its  lowest  terms  when  no  number  greater 
than  1  will  divide  both  terms. 

1.  Eeduce  f  to  its  lowest  terms. 

SOLUTION. — Dividing  both  terms  of  f  by  2,  the  result  is  |. 

2.  Reduce  f  to  its  lowest  terms. 

3.  Reduce  f  to  its  lowest  terms. 

4.  Reduce  %  to  its  lowest  terms. 

5.  Reduce  -|  to  its  lowest  terms. 

SOLUTION.— Dividing  both  terms  of  |  by  2,  the  result  is  |;  dividing 
both  terms  of  f  by  2,  the  result  is  \. 

Reduce  to  their  lowest  terms: 
6-  A,      f,      |,      T\>     A>     «• 

*•    A?      15'        7'        A?      To"'      Tf-     -' 

8-  A,  «,  If  H.  If'  tt- 

9-  A,  «,  it,  H,  H-  «• 

10-  &,  W,  it,  tt,  «,  fi- 
ll- it,  if-  li,  tt,  M,  If- 1 

1018          20         24         25         25         35 
'    "2T'      "2T'      "ST?      ^7'      ¥5"?      1^"' 

is-  «,    H,    if,    »,    «,    ff- 

14.  If,     If,     tt,     tf,     ff,     H- 


5G      "  KAY'S  NEW  INTELLECTUAL  ARITHMETIC. 

LESSON  XXVIII. 

1.  Ecducc  £  to  fourths. 

SOLUTION.— In  1  there  are  four-fourths;  then,  in  £  there  is  $  of 
4  fourths  =  2  fourths. 

2.  Eeduce  -|  to  sixths.          5.  Eeduce  •§-  to  twelfths. 

3.  Reduce  J  to  eighths.        6.  Eeduce  £  to  ninths. 

4.  Eeduce  i  to  tenths.          7.  Eeduce  \  to  twelfths. 

8.  Eeduce  •§  to  sixths. 

SOLUTION.— 1  — f;  then,  $•  =  £,  and  f  =  f. 

9.  Eeduce  f  to  ninths.     Eeduce  f  to  twelfths. 

10.  Eeduce  J  to  eighths.     Eeduce  j  to  twelfths. 

11.  Eeduce  f  to  tenths.     Eeduce  f  to  fifteenths. 

12.  Eeduce  -|  to  twentieths.    Eeduce  f  to  twenty-fifths. 

13.  Eeduce  §  to  thirtieths.     Eeduce  -f  to  thirty -fifths. 

14.  Eeduce  J-  to  twelfths.     Eeduce  |  to  eighteenths. 

15.  Eeduce   f   to    fourteenths.      Eeduce   ^   to   twenty- 
firsts. 

16.  Eeduce  ^  to  twenty-eighths.      Eeduce   f  to  thirty- 
fifths. 

17.  Eeduce    -|    to    sixteenths.      Eeduce    f    to   twenty- 
fourths. 

18.  Eeduce  f  to  thirty-seconds.     Eeduce  f  to  fortieths. 

19.  Eeduce    |    to   eighteenths.      Eeduce    f    to    twenty- 
sevenths.     ^ 

20.  Eeduce  ^  to  thirty-sixths.     Eeduce  ^  to  forty-fifths. 

21.  Eeduce  -f  to  fifty-fourths.     Eeduce  |  to  sixty-thirds. 

22.  Eeduce  ^  to  twentieths.     Eeduce  ^  to  thirtieths. 

23.  Eeduce  -f%  to  twenty-fourths.     Eeduce  -j%  to  thirty- 
sixths. 


FRACTIONS.  57 

LESSON  XXIX. 

NOTE. — When  two  or  more  fractions  have  the  same  denominators^ 
they  are  said  to  have  a  common  denominator.  The  common  denom- 
inator may  be  found  by  multiplying  the  denominators  together,  or 
by  finding  their  least  common  multiple,  that  is,  the  least  number 
that  can  be  divided  by  them. 

1.  Eoduce  f  and  f  to  equivalent  fractions  having  a 
common  denominator. 

SOLUTION. — The    common    denominator   is    3  X  4  =  12.     1  =  {f, 

*=A>I=A:  i =*i.  *=&.!= A- 

Reduce  to  equivalent  fractions  having  a  common  de- 
nominator : 


2. 

£ 

and 

t' 

£ 

and 

£. 

| 

and 

t 

3. 

i 

and 

i- 

i 

and 

i 

J 

and 

£. 

4. 

f 

and 

1- 

1 

and 

i- 

f 

and 

t 

5. 

1 

and 

f 

1 

and 

t 

i 

and 

t- 

6. 

1 

and 

fr 

f 

and 

f 

i 

and 

f 

7. 

t 

and 

f 

1 

and 

8 

T- 

1 

and 

f 

8. 

f 

and 

1 

f 

and 

I 

i 

and 

f 

9. 

* 

and 

A- 

1 

and 

A- 

-j 

a,nd 

A- 

10. 

£,  |,  and  i.  t,  J, 

and 

i 

,t 

11. 

I,  |,  and  f 

f.  f, 

and 

| 

. 

12. 

i 

li 

,  and 

j 

. 

13.  Reduce  f  and  f  to  equivalent  fractions  having  the 
least  common  denominator. 

SOLUTION. — The  least  common  denominator  is  12.    1  =  -^;  .|  — 1|. 
Reduce  to  equivalent    fractions   having    the  least  com- 
mon denominator: 

14.  £    and    J.     £     and     £.     J  and     J. 

15.  |    and    f     |     and     f.     f  and     f 


58       RAY'S    NEW  INTELLECTUAL  ARITHMETIC. 

16.  |-    and    -|.     £     and     -J.     -J  and  y^-. 

17.  ^,  ^,  and     \.     £,  J,  and    £. 
\18.     |,  f,  and     £.     f,  f,  and    £. 

19.  |,  |,  and     f     |,  |,  and    f. 

20.  |,  £,  and  yV     |-,  |,  and  ^.  ^ 

21.  £,  i,  £,  and     f     ^,  -J-,  £,  and  TV 

22.  I,  f,  I,  and    f     £,  J,  |,  and  yV 

23.  f,  f,  |,  and  .&.•.'£,  £,  f,  and  ^. 

24-     i  i^  i?  i?  and  f     1,  f,  f,  £,  and  |f 
25.     i,  f,  f ,  f ,  |,  A,  and  i|. 

t* 
LESSON  XXX. 

1.  James  divided  a  melon,  giving  to  his  sister  -J,  and  to 
his  brother  \ :  what  part  did  he  give  away  ? 

SOLUTION.     He  gave  away  \  -)-  \.     ^  =  f;  f  +  4  =  f  of  a  melon. 

2.  Thomas  gave  j  of  a  dollar  for  a  knife,  and  \  of  a 
dollar  for  a  ball :  how  much  did  he  give  for  both  ? 

3.  A  yard  of  flannel  costs  S-J-,  and  a  yard   of  cloth,  $| : 
how  much  do  both  cost? 

4.  I  give  Mary  -J,  Jane  ^,  and  William  \  of  an  orange : 
how  much  do  I  give  to  all? 

5.  What  is  the  sum  of  \  and  \  ? 

6.  Thomas  bought  a   copy-book  for   Sy1^,  and  a  reader 
for  %\\  how  much  did  both  cost? 

7.  Bought    \\  yards  of  muslin  at    one   store,    and    2J 
yards  at  another:  how  many  yards  did  I  purchase? 

SOLUTION.     1  \  —  f ;  2}  =  |.     I  purchased  f  -f  f  =  3^  yards. 

8.  I  planted   2^  acres  of  ground  in  corn,  and  8|  acres 
in  oats :  how  many  acres  did  I  plant  ? 


FRACTIONS.  59 

9.  John  bought  a   knife   for  $£,  a  slate  for  &J,  and  a 
book  for  $| :  how  much  did  all  cost  ? 

10.  Add     %  and     f.  |  and  f.         f  and  f. 

11.  Add     £  and     f.  \  and  \.         \  and  f  * 

12.  Add     \  and     f  f  and  f  X  J  and  |. 

13.  Add     I  and     f.  |  and  f.         |  and  |.  ^ 

14.  Add  if  and  2£.  £,  J,  £,  and  f 

15.  Add  3|  and  4£. 

SOLUTION.     3-f  4  =  7,  f +  $  =  1J;  7  + 1$  =  8J. 

16.  Add  4f  and  5J.  ^  1|,  2f,  |,  and  6TV 

17.  Add  5f  and  4f         |,  3|,  4^  and  5f. 


LESSON 


1.  James  received   1  an   orange    and   Charles,  J:    how 
much  more  did  James  receive  than  Charles? 

SOLUTION.     James  received    more    than    Charles    \  —  |.      1  =  1; 
\  =  l-     f  —  |  =  i  of  an  orange. 

2.  If  I  give  to  Mary  ^  of  an   apple,  and   to   Jane  ^, 
how  much  more  will  Mary  have  than  Jane? 

3.  James  bought   2  melons;    he  gave  to  Lucy  half  of 
the  first,  and  to  Jane  two-thirds  of  the  second  :  what  part 
of  a  melon  had  Jane  more  than  Lucy  ? 

4.  If  a   bushel   of  wheat    cost   $1J,  and   a   bushel   of 
corn,  $|,  "how  much  will  the  wheat  cost  more  than  the 
corn? 

5.  Joseph    bought  a  quart  of  chestnuts,  and  gave  \  to 
his  mother  and  \  to  his  sister:    how  much  more  did   he 

give  his  mother  tha'n  his  sister? 

r 


60        KAY'S   NEW   INTELLECTUAL  AKITHMETIC. 

6.  Jane  gave  If  oranges  to  Mary,  and   2J  to   Lucy: 
how  much  more  did  she  give  to  Lucy  than  to  Mary? 

SOLUTION.     1|  =  |;  2^  =  |.     Jane   gave   Lucy  more  than  Mary 
|  —  J,  or  T7£  of  an  orange. 

7.  Take     I  from     f       J  from     J.       £  from     J. 

8.  Take     f  from     f       J  from     f.       £  from     f. 

9.  Take     J  from     f.       f  from     |.       |  from     J/~ 

10.  Take     £  from     }.       £  from     f.       J  from     f 

11.  Take     f  from     f.       f  from     f.       f  from    £    ^ 

12.  Take     %  from     f.       f  from     f.       £  from  2|. 

13.  Take  2|  from  5f 

SOLUTION.     We  can  not  subtract  f  from  g ;  but  we  can  take  1  from 
5,  and  can  subtract  f  from  11.     1£  —  | '-  =  |,  4  —  2  =  2;  2  +  |  =  2|. 

14.  Take  3J  from  7f.     4J  from  8f 

15.  Take  5f  from  7f.     6|  from  8f     74  from  9|. 


LESSON  XXXII. 

1.  Mary  divided  a  quart  of  pecans,  giving  Ann  £,  and 
Jane  \  of  them:  what  had  she  left? 

SOLUTION. — Mary  gave  away  £  +  \  =  ^  of  a  quart;  she  had  left 
II  —  &  =  &  of  a  quart. 

2.  After  taking  away  \  and  -J  of  an  apple,  what  will  be 
left? 

3.  Thomas  wishes  to  divide  an  orange,  and  give  Ann 
},  and  Lucy  -|:  how  much  will  he  have  left? 

4.  A  farmer  sows  %  of  a  field  in  rye,  ^  in  barley,  and 
the  remainder  in  oats:  how  much  does  he  sow  in  oats? 

5.  A  man  having  72  miles  to  travel,  went  £   the   dis- 


FRACTIONS.  61 

tance  the  first  day,  -|  the  second,  and  the  remainder  the 
third  day :  what  part  did  he  travel  the  last  day,  and  how 
far?  </^ 

6.  David  bought  a  pound   of  figs :    he  gave  -J  to   his 
mother,  J   to  his   sister,  and  ^  to  his  brother :   what  part 
had  he  left? 

7.  A  farmer  had  1^  bushels  of  wheat :    he  gave  to  one 
poor  man  %  of  a  bushel,  and    to  another  ^  of  a  bushel : 
how  much  wheat  was  left? 

8.  James  had  J  of  a  pound  of  raisins :    he  gave  to  his 
brother  half  of  a  pound,  and  to  his  sister  \  of  a  pound : 
how  much  had  he  left? 

9.  A  lady  bought  3J  yards  of  muslin  at  one  store,  and 
2]-  yards  at  another :  after  using  1^  yards,  how  much  had 
she  left? 

-^  10.  William's  father  gave  him  $f :  he  gave  to  a  poor 
person  $-$•;  for  apples,  $Jg-;  and  for  a  book,  $£:  what  part 
of  a  dollar  had  he  left? 

11.  James'  mother  gave  him  a  book:    he  read  the  first 
day  -J-;    the  second,  ^;    the  third,  -J-;  and  the  fourth,  the 
remainder:  what  part  did  he  read  the  fourth  day? 

12.  A  farmer  has  a  flock  of  84  sheep  in  four  fields:  the 
first  contains  -J-;  the  second,  £;  and  the  third,  \  of  them: 
how  many  does  the  fourth  field  contain? 

13.  Daniel    spends    -^  of  his  time    in    sleep,  \  of  it  at 
school,  y1^-   in    reading,  and   -fa  in    learning  music :  what 
part  of  his  time  is  not  employed? 

14.  A  pole  is  standing  in  a  pond;  -|  of  it  is  in  the  air, 
and  ^  in  the  water:  what  part  is  in  the  earth? 

15.  A  student  devotes  ^  of  his  time  to  sleep,  ^  to  study, 
2^  to  reading,  ^  to  exercise,  and  y1^-  to  deeds  of  charity : 
what  part  of  his  time  rs  unemployed? 

16.  After  spending  £  and  ^  of  my  money,  and    losing 
jL,  I  had  $8  remaining:   how  much  had  I  at  first? 


62        KAY'S    NEW  INTELLECTUAL  ARITHMETIC. 


LESSON   XXXIII. 


1.  A  mother  gave  each  of  her  3  children 
how  many  oranges  did  it  take? 


an  orange 


SOLUTION.  —  It  took   3   times  \   an  orange,  which  are  f.     f  =  1  1 
oranges. 

2.  John  fed  5  horses,  giving  to  each  ^  a  peck  of  oats  : 
how  many  pecks  did  it  take? 

3.  James  gave  £  of  an  orange  to  each  of  his  4  sisters  : 
how  many  did  it  take? 

4.  John  gave  %  of  a  pine-apple  to  each  of  his  2  broth- 
ers :   how  many  did  he  give  to  both  ? 

5.  What  are  4  times  4? 

3  V/ 

SOLUTION.  —  4  times  f  are  |  =  2f  . 

6.  Thomas  gave  \  of  an  apple  to  each  of  his  6  play- 
mates :   how  many  apples  did  it  take  ? 

7.  Charles  gave  f  of  a  pint  of  chestnuts  to  each  of  his 
2  brothers  :   how  many  pints  did  it  take  ? 

8.  Mary  gave  f  of  an  orange  to  each  of  her  3  broth- 
ers :   how  many  oranges  did  it  take  ? 


9. 

What 

are 

6 

times 

i? 

7 

times 

I? 

8 

times 

F 

10. 

What 

are 

3 

times 

P 

5 

times 

I? 

6 

times 

F 

11. 

What 

are 

3 

times 

P 

4 

times 

f? 

5 

times 

T'? 

12. 

What 

are 

5 

times 

i? 

2 

times 

V 

4 

times 

F 

13. 

What 

are 

2 

times 

¥? 

4 

times 

1? 

5 

times 

F 

14. 

What 

are 

8 

times 

|? 

0 

times 

I? 

7 

times 

F 

15. 

What 

are 

5 

times 

f? 

8 

times 

V 

9 

times 

F 

16. 

What 

are 

7 

times 

i? 

(1 

times 

•£? 

8 

times 

f? 

17. 

What 

are 

3 

times 

F 

4 

times 

f? 

6 

times 

f? 

18. 

What 

are 

7 

times 

4? 

8 

times 

|? 

9 

times 

4  ? 

FRACTIONS.  63 

LESSON  XXXIV. 

1.  If  3   bushels   of  corn    cost   $1,  what  will  2  bushels 
cost? 

SOLUTION. — 1  bushel  will  cost  $^;  then,  2  bushels  will  cost  2  times 

H=*f 

2.  If  3  bushels  of  wheat  cost  $2,  what  will  2  bushels 
cost  ? 

3.  If  3  barrels   of  cider   cost   $8,  what    will  2  barrels 
cost? 

4.  If  4  barrels  of  apples   cost   $9,  what  will  2  barrels 
cost? 

5.  If  5  apples  cost  2  cents,  what  will  4  apples  cost? 

6.  James    bought    3    lemons    for    7    cents,    how    much 
would  2  lemons  cost? 

7.  William  bought  5  quarts  of  chestnuts   for  18  cents ; 
at  that  rate,  what  did  4  quarts  cost? 

8.  If  4  pounds  of  cheese  sell  for  30  cents,  what  should 
3  pounds  sell  for? 

9.  What  are  f  of  9  ? 

SOLUTION. — \  of    9   is   |;  then,  £  of  9  ure  3  times  |,  which  tire 


10. 

What 

arc 

4 

of 

6? 

7? 

8? 

9? 

11? 

11. 

What 

are 

t 

of 

5? 

7? 

10? 

11? 

12? 

12. 

What 

arc 

| 

of 

8? 

9? 

10? 

11? 

12? 

13. 

What 

are 

l 

of 

5? 

7? 

9? 

11? 

12? 

14. 

What 

are 

l 

of 

6? 

7? 

8? 

10? 

12? 

15. 

What 

are 

9 
TIT 

of 

6? 

8? 

9? 

11? 

12? 

16. 

What 

are 

vt 

of 

3? 

5? 

8? 

9? 

12? 

17. 

What 

are 

tt 

of 

7? 

8? 

9? 

10? 

11? 

64        HAY'S   NEW   INTELLECTUAL  ARITHMETIC. 

18.  If  4  men  perform  a  piece  of  work  in  8  days,  how 
long  will  it  take  5  men? 

SOLUTION. — It  will  take  1  man  4  times  8  days  =  32  days;    then, 
it  will  take  5  men  £  of  32  days  =  Of  days. 

19.  If  one  barrel  of  flour  serve  8  persons  20  days,  how 
long  will  it  last  11  persons? 

20.  If  7  men  can  do  a  piece  of  work  in  5  days,  how 
long  will  it  require  8  men? 

21.  If  2  men  build   a  wall   in  12  days,  how  long  will 
it  take  7  men  ? 

22.  If  it  require  11  days,  of  8  hours  each,  to  do  a  cer- 
tain work,   how  many  days,    of  10   hours    each,  will   bo 
required  to  accomplish  the  same? 

23.  A   man   paid    37  cents    for  riding  8  miles:    at  the 
same  rate,  what  will  it  cost  to  ride  11  miles? 

24.  If  2  pipes  of  a  certain  size  empty  a  cistern  in  17 
minutes:  in  what  time  will  3  pipes  empty  it? 

25.  If  18  bushels  of  oats  last  5  horses  one  week,  how 
many  bushels  will  7  horses  require? 

26.  If  a  laborer  receive  5  bushels  of  wheat  for  7  days' 
work,  how  much  should  he  receive  for  11  days? 

27.  If  a  carpenter    earn    $8  in  5  days,  how  much  will 
he  earn  in  9  days? 

28.  A  pole,  18  feet  long,  is  two-sevenths  in  the  earth, 
the  rest  in  the  air:  what  is  the  length  of  each  part? 

29.  Three    men    found  a  bag    containing   $15:    A  got 
|,  B  |,  and  C  the  rest :  what  was  the  share  of  each  ? 

30.  If  3  ounces  of  snuff  cost  36  cents,  what  should  be 
charged  for  %  of  an  ounce? 

31.  A  watchmaker  sold  a  watch  for  $18,  and  lost  f  of 
its  value :  how  much  did  he  lose  ? 

32.  A  watchmaker  sold   a  watch    for    $45,  and   gained 
of  its  cost :  what  was  its  cost  ? 


FKACTIONS. 


65 


LESSON  XXXV. 


1.  William  gave   11   oranges   to  each  of  his  2  sisters  : 
how  many  oranges  did  it  take? 

SOLUTION.  —  l|  =  f.      It   took  2   times  f  oranges,  which  are  f  = 
3  oranges. 

2.  How  many  are     3  times  2^? 
SOLUTION.  —  2£  —  f  .     3  times  |  are  3-f-  =  7£. 


3.  If  1   bushel  of  wheat  cost 
cost? 


4.  How  many  are  3  times  1-J  ? 

5.  How  many  are  3  times  3^? 

6.  How  many  are  5  times  2|? 

7.  How  many  are  8  times 


8.  If  1  bushel  of  barley  cost 
cost?    4  bushels? 


what  will  2  bushels 


2  times  2|  ? 
4  times  41? 
6  times  3f  ? 
9  times  4|? 

what  will   3  bushels 


9.  How  many  are     5  times 

10.  How  many  are     2  times  If? 

11.  How  many  are     4  times  3^? 

12.  How  many  are     6  times  3£? 

13.  How  many  are     7  times  2^? 

14.  How  many  are  10  times  If? 

15.  How  many  are  12  times  3|? 


6  times 
3  times 
5  times  3-|? 

8  times  3f  &£>- 

9  times  2f  ? 
10  times  3? 


SOLUTION.— -12  times  3  —  36,  12  times  f  are  -^  —  9;  36  -f-  9  ^rjg^-— -- 

16.  If  a   family  consume   31-   barrels   of   flour   in   one 
month,  how  much  will  they  require  for  3  months? 

r~i      r 


Int.  5. 


"ft     *     **      " 


66 


BAY'S  NEW  INTELLECTUAL  ARITHMETIC. 


17. 

18. 
,19. 
20. 

How  many  are     4 
How  many  are     2 
How  many  are     6 
How  many  are     7 

times  3|?              5  times  3f  ? 
times  6f  ?               3  times  2f  ? 
times  4^?               6  times  3f  ? 
times  4|?               8  times  3f  ? 

21. 

How  many  are     9 

times  If?              9  times  3£? 

22. 

Three 

times 

4| 

are 

how 

many  ? 

23. 

Foui- 

times 

4f 

are 

how 

many  ? 

24. 

Five 

times 

4| 

are 

how 

many? 

25. 

Four 

times 

6* 

are 

how 

many  ? 

26. 

Five 

times 

6i 

are 

how 

many? 

27. 

Six 

times 

*i 

are 

how 

many? 

28. 

Seven 

times 

6f 

are 

how 

many  ? 

29. 

Four 

times 

7f 

are 

how 

many  ? 

30. 

Five 

times 

77 

are 

how 

many  ? 

31. 

Six 

times 

7| 

are 

how 

many  ? 

32. 

Four 

times 

8t 

are 

how 

many? 

33. 

Five 

times 

H 

are 

how 

many  ? 

34. 

Six 

times 

81 

are 

how 

many  ? 

35. 

Three 

times 

9| 

are 

how 

many  ? 

36. 

Five 

times 

9| 

are 

how 

many  ? 

37. 

Seven 

times 

9f. 

are 

how 

many? 

38. 

Two 

times 

10* 

are 

how 

many? 

39. 

Five 

times 

10f 

are 

how 

many  ? 

40. 

Six 

times 

lOf 

are 

how 

many? 

41. 

Nine 

times 

10-j^ 

are 

how 

many  ? 

42. 

Ten 

times 

9f 

are 

how 

many? 

43. 

Twelve 

times 

ll^Y 

are 

how 

many? 

.-' 


9-f 


44.  How  many  are 

45.  How  many  are 

46.  How  many  are 

47.  How  many  are  10|-     multiplied  by  11? 

48.  How  many  are  12  J     multiplied  by  10? 


multiplied  by     6? 
7f    multiplied  by     7? 
multiplied  by  11? 


• 


FRACTIONS.  67 

LESSON  XXXVI. 

1.  Bought  5  boxes  of  raisins,  at  $4f  a    box ;    paid  for 
them  with  flour,  at  $6  a  barrel :  how  many  barrels  did  it 
take? 

SOLUTION. — The  raisins  cost  5  times  $4|  — $24;  then,  it  took  as 
many  barrels  of  flour  to  pay  for  them  as  $6  are  contained  times  in 
$24,  which  are  4. 

2.  Bought  6  gallons  of  wine,  for  $4|  a  gallon,  and  paid 
for  it  with  raisins,  at  $5  a  box:  how  many  boxes  did  it 
take? 

3.  Bought  7  kegs  of  tobacco,  for  $5-f-  a  keg,  and  paid 
for  it  with  paper,   at    $6  a   ream :    how  many  reams  did 
it  take? 

4.  Five     times    5|   are   how   many  times   6? 

SOLUTION.— 5  times  5f  =  28.    28  H-  6  =  4f . 

5.  Four    times   4f   are   how   many  times  3?     5?     6? 
8?    9?     10? 

6.  Six       times    6-f   are   how   many  times  4?     5?      7? 
8?     9?     10? 

7.  Five     times    5|   are   how   many  times  4?     6?     8? 
9?     10? 

8.  Eight  times   8£   are    how   many  times  5?     6?     7? 
9?     10? 

9.  Seven  times   6^    are   how   many  times  5?     8?     9? 
10? 

10.  Ten      times    5|   are   how   many  times   6?     7?     8? 
9?     10? 

11.  Eight  times    8f   are   how   many  times   6?     7?     9? 
10?     11? 


68        KAY'S   NEW  INTELLECTUAL  ARITHMETIC. 

12.  Seven   times   7$   are   how  many  times  5?    6?    8? 
9?     10? 

13.  Five      times   5f   are   how  many  times  6?     7?     8? 
9?     10?    / 

14.  Nine     times   6J   are   how  many  times  5?    7?    8? 
10?    11? 

15.  Seven   times   7f   are   how  many  times  5?     6?    9? 
10?     12? 

16.  Bought  4|  yards  of  cloth,  at  $3  a  yard,  and  paid 
for  it   with  cheese,  at  $7   a  hundred- weight :    how  many 
hundred-weights  did  it  take? 

SOLUTION. — The  cloth  cost  $3  X  4f  =  $14;  it  took  as  many  hun- 
dred-weights as  $7  are  contained  times  in  $14,  which  are  2. 

17.  Bought  44  pounds  of  nails,  at  5  cents  a  pound,  and 
paid  for  them  with  eggs,  at  12  cents  a  dozen :  how  many 
dozen  did  it  take? 

18.  Bought  7-f-  pounds  of  sugar,  at  7  cents   a  pound, 
and  paid  for  it  with  chickens,  at  27  cents  each  :  how  many 
did  it  take?        / 

19.  Bought  9f  pounds   of  sugar,  at  7  cents  a  pound, 
and  paid  for  it  with  eggs,  at  13  cents  a  dozen :  how  many 
dozen  did  it  take? 

20.  How   many  pounds   of  rice,  at   7   cents   a   pound, 
can  I  get  for  8|  yards  of  calico,  at  9  cents  a  yard  ? 

21.  How  many  barrels  of  flour,  at  $6  a  barrel,  must 
be   given  in   exchange   for   4^   yards   of  cloth,  at   $7  a 
yard  ? 

22.  Bought  5f  pounds  of  sugar,  at   7   cents   a  pound, 
and  paid   for  it  with   raisins,  at  6   cents  a  pound:   how 
many  pounds  did  it  take? 

23.  How  many  dozen   eggs,  at   12   cents  a  dozen,  will 
pay  for  lO^J  pounds  of  sugar,  at  11  cents  a  pound? 


FRACTIONS. 


LESSON  XXXVII. 

1.  Mary,  having   £  an    orange,  gave  her  brother  |  of 
what  she  had :  what  part  of  an  orange  did  she  give  him  ? 

SOLUTION. — She  gave  to  her  brother  ^  of  |  an  orange,  which  is  £ 
of  an  orange. 

2.  James  divided  J  of  an  apple  equally  between  his  two 
brothers :  what  part  did  each  receive  ? 

3.  If  J  of  an  orange  is  divided  into  2  equal  parts,  what 
is  1  of  the  parts  called  ? 

4.  If  J  of  an  apple  be  cut  into  3  equal  parts,  what  part 
of  the  apple  will  each  piece  be  ? 

5.  If  £  of  an  apple  be  divided  into  5  equal  parts,  what 
is  each  part  called? 

6.  If  you  divide  an  orange  into  4  equal  parts,  and  cut 
each  part  into  3  equal  pieces,  what  will  1  piece  be  called  ? 

What  single  fraction  equals: 

SOLUTION. — \  of  \  =  ^. 

8.  J  of  £?       J  of  J?      £  of  £?       J  of  J?      J  of  I?, 

9.  J  of  |?      J  of  £?       |  of  |?       J  of  £?      I  of  j? 
i  of  J? 

10.  J  of  J?      i  of  |?      J  of  J?      |  of  |?      £of£? 
iofi? 

11.  Thomas  has  }  of  an  apple,  and  wishes  to  give  his 
brother  £  of  what  he  has :  what  part  of  the  whole  apple 
must  he  give  him? 

SOLUTION. — He  must  give  him  \  of  |  of  an  apple;  \  of  \  =  };  then 
|  of  f  is  3  times  £  =  f . 


70         KAY'S  NEW  INTELLECTUAL  ARITHMETIC. 

12.  Daniel  has  f  of  a  melon  to  divide  equally  between 
his  brother  and  sister :  how  must  he  divide  it,  and  what 
part  of  the  whole  will  each  receive? 

13.  What  is  i  of  f? 

SOLUTION. — 1  of  £  =  Ty,  then,  1  of  f  =  T23. 

What  is  i  of  |?     ioff?     £off?      Joff? 

15.  What  is  I  of  £?     |  of  f  ?      |off?     \  of  f  ? 

16.  What  is  i  of  f?    |  off?    TV°fi?    TT°ft? 

17.  Edward    has  £  of  a  melon,   and   gives    his   sister 
I   of  what   he   has:    what  part  of  the  melon   does  she 
receive  ? 

SOLUTION. — She  receives  f  of  f  of  a  melon.    $  of  $  is  TV,  then, 
|  of  |  are  2  times  T\  =  1§s. 

18.  What  are  f  of  f  ? 

SOLUTION. — J  of  \  is  J;  then,  §  of  f  are  f  =  £. 

19.  What  are  |  of  f  ?    f  of  f  ?     f  of  f  ?    f  of  f  ?    „, 

20.  What  are  f  of  f  ?    f  of  f  ?     f   of  f  ?    f  of  ^? 

21.  What  are  f  of  f  ?    f  of  ^?     f   of  -f  ?    f  of  |  ? 

22.  What  are  f  of  |?     f  of  |  ?    ft  of  £?     f  of  f  ? 

23.  What  are  |  of  |?    |  of  ^-?    Hofl?    TofTT? 

24.  A  person,  owning  |  of  a  ship,  sold  f  of  his  share : 
what  part  of  the  ship  did  he  sell  ? 

25.  A  banker,  owning  |  of  the  entire  stock  of  a  bank, 
disposed  of  ^  of  his  share :   what  part  of  the  stock  did 
ho  sell? 

26.  If  a  man  sell  %  of  -f$  of  his  stock  of  merchandise, 
what  amount  does  he  sell? 

27.  I  buy  -fa  of  |  of  the  shares  in  a  corporation,  how 
much  do  I  buy? 

28.  |  of  ^  of  j^  are  how  many  ? 


FRACTIONS.  71 

LESSON  XXXVIII. 

I.  If  1  yard  of  cloth    is  worth   2£  bushels  of  wheat, 
what  is  £  a  yard  worth? 

SOLUTION.— 2£=  f ;  |  of  f  =  £,  or  1|  bushels. 
What  single  fraction  will  represent: 

2.1.  of  2^?     JoflJ?     Jofl}?     Jof2£?     i 
^  3.  iof4f?    |of5J?    |  of  4?     foflf?     f 

4.  f  of  41?     fof2f?     fofSi?    |  of  24?    fof4f? 
-^5.  If  2  yards  of  cloth  cost  $1^,  what  will  3  yards  cost? 

6.  If  3  yards  of  cloth  cost  $51,  what  will  2  yards  cost? 

7.  If  4  gallons  of  molasses  cost  $3|,  what  will  3  gal- 
lons cost? 

8.  If  7  pounds  of  sugar  cost  $1^-,  what  will  4  pounds 
cost? 

9.  If  4  pounds  of  butter  cost  $1J,  what  will  7  pounds 
cost? 

10.  If  7  yards  of  cloth  cost  $5-|,  what  will  be  the  cost 
of  3  yards?     Of  4  yards? 

II.  If  2  barrels  of  cider   cost  $4f,  what  part  of  that 
sum  will  5  barrels  cost? 

12.  If  5  gallons  of  oil  cost  $2|,  what  part  of  that  sum 
will  7  gallons  cost?        \/ 

13.  If  3  bottles  of  wine  cost  $2J,  what  will  be  the  cost 
of  8  bottles?     Of  10  bottles? 

14.  A  man    can  perform  a  piece   of  work   in  3J  days, 
of  10  hours  each :  how  many  days,  of  7  hours  each,  will 
it  take  ? 

15.  If  a  man  can  do  a  piece  of  work  in  14|  days,  work- 
ing 5  hours  a  day,  how  many  days  will  it  take,  working 
8  hours  a  day? 


72        RAY'S   NEW  INTELLECTUAL  ARITHMETIC. 

LESSON  XXXIX. 

1.  A  jockey,  by  selling  a  horse  for  $45,  gained  J  of  the 
cost  :  what  was  the  cost  ? 


SOLUTION.  —  $45  are  f  -f-£  =  f  of  the  cost;  then,  £  of  the  cost  is 
£  of  $45  =  $5,  and  the  cost  is  8  times  $5  =  $40. 

2.  James  gave  his  brother  4  marbles,  which  were  J  of 
all  he  had  :  how  many  had  he  ? 

3.  Thomas   sold  a  knife  for  15  cents,   which  was  f  of 
its  cost:  how  much  did  it  cost? 

4.  William  lost  6  marbles,  which  were  |  of  all  he  had  : 
how  many  had  he? 

5.  I  sold   a   horse   for   $42,  which  was   -f   of  its  cost: 
what  was  its  cost? 

6.  A  grocer  sold  a  lot  of  flour  for  $40,  which  was  j  of 
the  cost:  what  was  the  cost? 

7.  Sold  a  horse  for  $56,  which  was  |-  of  the  cost  :  what 
was  the  cost? 

8.  A  man  sold  a  watch  for  $28,  which  was  f  of  its  cost  : 
what  was  its  cost? 

9.  A  man  sold  a  pony  for  $45,  which  was  |  of  its  cost  : 
what  was  the  cost? 

10.  A  man  purchased  a  horse  :  after  paying  J  of  the 
price,  he  owed  $20  :   what  was  the  price  of  the  horse  ? 
How  much  money  did  ho  pay? 

11.  Alexander  sold  a  book  for  25  cents,  and  lost  ^  of 
the  cost:  what  was  the  cost? 

12.  In  an  orchard   there   arc   12  cherry-trees  :  the  re- 
maining fy  of  the  orchard  are  apple-trees  :  how  many  trees 
are  there  in  the  orchard? 

13.  Four-fifths  of  a  stick   are  under  water,  and  6  feet 
arc  out  of  water  :  how  long  is  the  stick  ? 


FRACTIONS.  73 

14.  There  is  a  pole,  f  of  which  are  in  the  earth,  and  12 
feet  are  in  the  air:  how  long  is  the  pole? 

15.  A  piece  of  timber  stands  ^  in  the  air,  and  5  feet  in 
the  ground :  how  long  is  the  entire  piece  ? 

16.  -J  of  a  pole  is  in  the  mud,  -|  are  in  the  water,  and 
14  feet  in  the  air :  how  long  is  the  pole  ? 

17.  A  man  gave  to  some  poor  persons  $4,  which  was  | 
of  his  money :  how  much  had  he  left  ? 

18.  At  $8  a  yard,  ^  of  the  cost  of  a  piece  of  cloth  was 
lost :  what  was  the  cost  ? 

19.  If  f  of  the  cost  of  a  horse  were  $64,  and  it  was 
bought  with  flour,  at  $4  a  barrel :  how  many  barrels  did 
it  take? 

20.  If  £  of  a  cask  of  wine  cost  $42,  how  much  flour,  at 
$8  a  barrel,  will  pay  for  a  whole  cask? 

21.  If  f   of  a  yard  of  muslin  cost  8  cents,  how  many 
yards  can  be  purchased  for  25  cents? 

22.  If  -f-  of  a   yard   of  cloth  cost  $4,  how   many  yards 
can  be  purchased  for  $12. 

23.  By  selling  5  yards  of  cloth  for  $12,  I  gained  £  of 
the  cost :  what  did  I  pay  per  yard  ? 

24.  If  f  of  a  pound  of  raisins  cost  9  cents,  how  many 
lemons,  at  2  cents  each,  will  pay  for  a  pound? 

25.  If  ^  of  a  pound  of  coffee  cost  16  cents,  how  many 
oranges,  at  4  cents  each,  will  pay  for  one  pound? 

26.  If  I    of  a   barrel    of   wine    cost    $42,    how    many 
barrels  of  cider,  at   $6   each,  will    pay  for    a   barrel   of 
wine? 

27.  If  f  of  a  barrel  of  sugar  cost  $12,  how  many  bar- 
rels of  flour,  at   $10  a  barrel,  will    pay  for  a   barrel   of 
sugar  ? 

28.  Sold  a  horse  for  $50,  which  was  f  of  his  cost :  paid 
for  him  with  cloth,  at   $4  a  yard :    how  many  yards  did 
I  give? 


74        RAY'S    NEW   INTELLECTUAL   ARITHMETIC. 

LESSON    XL. 

1.  12  is    %  of  how  many  times  5? 
SOLUTION.— 12  is  f  of  21;  21  -=-5  =  4$. 

2.  18  is  f  of  how  many  times  9? 

3.  16  is  J  of  how  many  times  9? 

4.  36  is  ^  of  how  many  times  8? 

5.  45  is  |  of  how  many  times  7? 

6.  24  is  |  of  how  many  times  5? 

7.  72  is    f  of  how  many  times  7? 
/    8.  81  is    j  of  how  many  times  3? 

9.  50  is  ^f-  of  how  many  times  4? 

10.  63  is    -J  of  how  many  times  5  ? 

11.  56  is    -|  of  how  many  times  7? 

12.  A  man,  having  12  bushels  of  grain,  divided  |-  of  it 
among   3  poor  persons  equally:    how  many  bushels  did 
each  receive? 

SOLUTION. — £  of  12   bushels   are   10  bushels.     Each   person   re- 
ceived $  of  10  bushels  =  3J  bushels. 

13.  A   boy,    having    25    apples,   kept    £    himself,   and 
divided  the  other  4  equally  among   6  companions:    how 
many  did  each  receive? 

14.  f  of  24  are  how  many  times    9? 

SOLUTION.— |  of  24  =  18;  18 --9  =  2. 

15.  J  of  24  are  how  many  times     8? 

16.  f  of  18  are  how  many  times     6? 

17.  J  of  27  are  how  many  times  10? 

18.  £  of  60  arc  how  many  times    7? 

19.  f  of  66  are  how  many  times     8? 

20.  I  of  48  arc  liow  many  times    9? 


FRACTIONS.  75 

21.  f  of  56  are  how  many  times     9? 

22.  ij-  of  63  arc  how  many  times  10? 
— ^23.     J  of  64  are  how  many  times     6? 

24.  |-  of  40  are  how  many  times    7  ? 

25.  J^1-  of  49  are  how  many  times     8? 

26.  ^  of  54  are  how  many  times     7? 

27.  Y-  °f  63  are  how  many  times     8? 

28.  -f  of  54  are  how  many  times     5  ? 

29.  f  of  42  are  how  many  times     8  ? 

30.  yL  of  55  are  how  many  times     6? 

31.  J  of  72  are  how  many  times  10? 

32.  |  of  96  are  how  many  times  11? 

i/ 

LESSON   XLI. 
1.  At  $|  a  yard,  how  much    cloth  can  be  bought  for 


SOLUTION. — For  $1,  2  times  1  yard  =  2  yard?  can  be  bought; 
then,  for  $J,  £  of  2  yards  =  f  of  a  yard  can  be  bought. 

2.  At  $J  a  yard,  how  much  gingham  can  be  purchased 
for  $J? 

3.  At  $%  a  yard,  how  much  alpaca   can  be  purchased 
for  $£? 

4.  At   $J   a   bushel,  how   much   corn    can   be   bought 
for  $£? 

5.  At   $§  a  yard,  how  much  cloth    can  be   purchased 
for  $|? 

SOLUTION. — For  $|,  J  a  yard  can  be  purchased,  and  for  $1,  f  of 
a  yard;  then,  for  $J,  \  of  f,  or  f  of  a  yard  can  be  purchased, 
and  for  $|,  |  =  1£  yards. 

6.  If  a  pound  of  coffee   is   worth   &f ,  how   much   can 
John  buy  for 


76        KAY'S    NEW   INTELLECTUAL   AKITHMETIC. 

7.  If  a  pound  of  tea  cost  $£,  how  much  tea  can  you 
purchase  for  $|? 

8.  At  $|  for  one  yard,  how  much  cloth  can  be  bought 
for  $|?     How  much  for  8f  ?     For  one  dollar? 

9.  One  bushel  of  rye  is  worth  £  of  a  bushel  of  wheat  : 
how  much  rye  is  worth  $  of  a  bushel  of  wheat?     How 
much  is  worth  1  bushel? 

10.  Divide  £  by  J. 

SOLUTION.  —  \  divided  by  ]  is  4  times  \  =  |  . 

11.  Divide  $  by  f  By  J.  By  J. 

12.  Divide  }  by  J.  By  £.  By  J. 

13.  Divide  |  by  f  By  f  By  f 

14.  Divide  £  by  f  . 

SOLUTION.—  £-=-£:=  J/  5   thcn»  f~*-f  =  i  of  V>  whidl  is  f  =  H- 

15.  Divide  f  by  f. 

16.  Divide  f  by  f.     By  f.     By  f. 

17.  Divide  f  by  f     By  f     By  f. 

18.  Divide  }  by  f     By  f     By  i. 

19.  Divide  j  by  f. 

SOLUTION.  —  g  H-  f  is  the  same  as  f  X  f  =  ||»  or  U- 


' 


20. 

Divide 

f  by 

* 

By 

1 
T- 

By 

f 

21. 

Divide 

&by 

f- 

By 

J. 

By 

f 

22. 

Divide 

«by 

TV 

By 

t 

By 

t 

23. 

Divide 

«by 

TT- 

By 

A- 

By 

f- 

24. 

Divide 

fby 

i 

» 

V 

1 

f 

by 

f. 

25. 

Divide 

I  by 

fr 

1 

by 

f 

1 

by 

f 

26. 

Divide 

¥  by 

» 

U 

by 

H- 

tt 

by 

1- 

27. 

Divide 

fby 

I- 

I 

by 

1 

f 

by 

f 

28. 

Divide 

V  by 

¥•• 

V 

by 

f. 

y 

by 

f. 

FKACTIONS.  77 

LESSON    XLII. 

1.  A  man,  having  10^  acres  of  land,  divided  it  equally 
among  his  6  children:  how  much  did  each  receive? 

SOLUTION. — W%  =  ty.      Each    received    J    of  ty    acres,  which  is 
y,  or  1|  acres. 

2.  If  2£  be  divided  by  7,  what  will  be  the  result? 

3.  How  many  times  is  6  contained  in  3J? 

4.  How  many  times  is  9  contained  in  6J? 

5.  Divide  8f  by    5.     7|  by  10. 

6.  Divide  4*  by  11.     8*  by  12. 

7.  If  1%  yards   of  ribbon   cost   6    cents,  what   will    1 
yard  cost?  ^ 

SOLUTION. — 1£  =  f.     $  a  yard  cost  £  of  6  cents  =  2  cents;  then,  1 
yard  cost  2  times  2  cents  =  4  cents. 

8.  If  1J  yards  of  cloth  cost  $4,  what  will  1  yard  cost? 

9.  If  a  man  travel  9  miles  in    1^    hours,  how  far  will 
he  travel  in  1  hour? 

10.  A  watch  was   sold   for  $18,  which   equaled    1-^   of 
what  it  cost  me:    how  much  did  it  cost? 

11.  A  grocer  sold  a  lot  of  flour  for  $25,  which  was  1J 
times  the  cost:  what  did  it  cost?     How  much  did  he  gain? 

12.  If  a  man  pays  $6  for  1|  yards  of  cloth,  what  is  the 
cost  of  1  yard? 

13.  If  a  man  receives  $10  for  2|  days  work,  how  much 
is  that  a  day?  ^ 

14.  If  a  man  receives  $12  for  6^  days  work,  how  much 
is  that  a  day? 

15.  How  many  arc     9  divided  by  3|? 

16.  How  many  are  10  divided  by  2|? 

17.  How  many  are  11  divided  by 


'8        KAY'S    NEW   INTELLECTUAL   ARITHMETIC. 

LESSON  XLIII. 

1.  If  a  yard  of  cloth  cost  $•§-,  how  many  yards  will 

:08t  $4f  ? 

SOLUTION. — 4|  =  -3r4-.     As  many  yards    as    §  are  contained  times 
n  ty,  which  are  ^=1%. 

2.  When  a  bushel  of  corn  costs  $-*-,  how  many  bushels 
;an  you  buy  for  $1J? 

3.  I  distributed  2§  bushels  of  wheat  among  a  number 
>f  poor  persons,  giving  to  each  f  of  a  bushel :  how  many 
)ersoris  were  there? 

4.  At  $J  a  yard,  how  many  yards  of  alpaca  can  be 
purchased  for  $3J? 

5.  At  $J  a  yard,  how  many  yards   of  cloth   can    be 
3urchased  for  $3J? 

6.  If  an  apple  cost  f  of  a  cent,  how  many  apples  can 
oe  purchased  for  3f  cents?     For  5J  cents? 

7.  If  a  yard  of  cloth  cost  $§,  how  many  yards  can  you 
purchase  for  $4£? 

8.  How  often  is  1J  contained  in  f  ?     In  f  ?     In  2|? 

9.  How  often  is  2J  contained  in  f  ?     In  f  ?     In  3£? 

10.  How  often  is  31-  contained  in  f  ?     In  f  ?     In  5f  ? 

11.  5J    is    i  of  what  number?     4-  of  what  number? 
„  12.  7J    is    ^  of  what  number?     |  of  what  number? 

13.  9^  are  4  of  what  number?     4  of  what  number? 

o  o  b 

14.  4§  are  f  of  what  number?    f  of  what  number? 

15.  3f  are  f  of  what  number?     f  of  what  number? 

V  16.  How  often    is    £  contained  in  3|?     In  5J?     In  4|? 

17.  How  often  are  f  contained  in  2f  ?     In  4f  ?     In  (U? 

18.  How  often  are  ^  contained  in  3f  ?     In  4f  ?     In  7f  ? 

19.  How  often  are  |  contained  in  4f  ?     In  5f  ?     In  s|? 

20.  How  often  are  f  contained  in  2^\?      In    6^?      In 
>f\?     In  lOf? 

SA 


FRACTIONS.  79 

21.  At  S-J  a  gallon,  how   many  gallons  of  vinegar  can 
you  buy  for  $2f  ?     For  $4£? 

22.  One  bushel  of  rye  is  worth  f  of  a  bushel  of  wheat : 
how  many  bushels  of  rye  can  be  bought  with  4J  bushels 
of  wheat?    With  8J  bushels? 


LESSON   XLIV. 

The  examples  in  this  lesson  are  to  be  solved  by  using 
the  following  tables,  where  applicable : 

I. — FRACTIONAL  PARTS  OF  12. 

2  =  4  6  =  4. 

3  =  4  8  =  f. 

4  =  4  9=f. 

10  =  f 

II. — FRACTIONAL  PARTS  OP  100. 

124  =  4  374  =  §. 

16|  =  4  50  =4. 
20  =4  624  =  f. 
25  =J  66f  =  §. 
33J  =  J  75  =f. 

87J  =  £ 

1.  Bought  f  of  a  dozen  shirts,  at  $24  a  dozen:   what 
did  they  cost? 

SOLUTION.— They  cost  f  of  $24  —  $18. 

2.  Bought  f  of  a  dozen  linen  collars,  at  $3  a  dozen : 
what  did  they  cost? 

3.  Bought  f  of  a  dozen  handkerchiefs,  at  $4  a  dozen  : 
how  much  did  they  cost? 


80        RAY'S    NEW  INTELLECTUAL  ARITHMETIC. 

4.  A  grocer  bought  6J  dozen  eggs,  for  16  cents  a  dozen : 
how  much  did  they  cost? 

5.  Bought  If  dozen  pairs  of  hose,  for  $21  a  dozen :  how 
much  did  they  cost?     What  did  each  pair  cost? 

SOLUTION.— lg  =  f ;  2f  =  Jj*.     They  cost  £  of  $J/=  $4.     Each  pair 
cost         of  $-U  =  $. 


6.  Bought  2J  dozen  copy-books,  for  $1£  a  dozen  :  how 
much  did  they  cost?     What  was  the  cost  of  each  book? 

7.  A   merchant    bought    6J    dozen    knives,   for   $1£    a 
.dozen:  what  did  they  cost?     What  did  1  knife  cost? 

V  8.  Paid  $5  a  set,  or  \  dozen,  for  2^  dozen  spoons:  what 
did  they  cost? 

9.  Bought  4J  dozen  spelling-books,  at  $2J  a  dozen :  how 
much  did  they  cost?    What  did  1  book  cost? 

10.  A  man    bought    2J  dozen    handkerchiefs,  for   $6f : 
how  much  was  that  apiece? 

SOLUTION.— 2£  =  f ;    6|  =  -2¥7-.     He  bought   \  of   a  dozen,   or  3, 
handkerchiefs,  for  \  of  $-2^  =  $f;    then,  1  handkerchief  cost  \   of 

*!=$*• 

11.  A  merchant  paid  $3^  for  7f  dozen  pairs  of  dam- 
aged hose,  and  sold  them  for  $-5^  a  pair:   how  much  did 
he  gain  on  each  pair? 

12.  A  merchant   paid   $15    for  2-|  dozen  silk  handker- 
chiefs, and   sold   them  for  $-f  apiece:    how  much  did  he 
gain  on  each  handkerchief?      How  much   on   the  whole 
lot? 

13.  Paid  $18f  for  6J  dozen  knives,  and  sold  them  for 
$2^  a  set,  or  \  doz. :  how  much  did  I  gain  ? 

14.  What  will    16  pounds  of  soap  cost,  at  12J  cents  a 
pound? 

SOLUTION. — 12J   cents  =  $|;    then,  16  pounds  will  cost  16  times 
$Jz=i/,  or  $2. 


FKACTIONS.  81 

15.  What  will  12  pounds  of  prunes  cost,  at  16§  cents 
a  pound? 

16.  What  will  24   yards  of  alpaca  cost,  at  37^  cents  a 
yard? 

17.  What  will  16  yards  of  flannel  cost,  at  62  J  cents  a 
yard? 

18.  What  will  15  pounds  of  coffee  cost,  at  33J  cents  a 
pound  ? 

19.  What  will  27  yards  of  flannel  cost,  at  66§  cents  a 
yard? 

\20.  What  will  15  yards  of  cloth  cost,  at  $1.66f  a  yard? 
21.  Paid   $12    for  coffee,   at    33J    cents  a  pound:    how 
many  pounds  did  I  buy? 

SOLUTION.  —  33  J  cents  =  $%.     I  bought  as   many   pounds  as   £  is 
contained  times  in  12,  which  are  36. 


22.  Paid  $1^  for  eggs,  at  12J  cents  a  dozen  :  how  many 
dozen  did  I  buy? 

23.  Paid    87£   for   flannel,   at    62J    cents  a  yard:  how 
many  yards  did  I  buy? 

24.  Paid    $8    for    flannel,  at    66§    cents    a   yard:    how 
many  yards  did  I  buy  ? 

25.  Multiply  32  by  12^. 

SOLUTION.—  12£  =  £  of  100;  then,  32  X  12£  =  32  -=-  8  X  100  =  400. 

26.  Multiply  18  by  50.  40  by  62J.  68  by  75. 

27.  Multiply  48  by  75.  24  by  37J.  51  by  33£. 

28.  Multiply  39  by  66f.  64  by  87f.  96  by  62J. 

29.  Divide    150  by  12  J. 

SOLUTION.—  150  -=-  12  \  =  150  X  8  +  100  =  12. 

30.  Divide  200  by  16§.          560  by  20.          250  by    25. 

31.  Divide  350  by  37^.          600  by  50.         750  by  62J. 

Int.  6. 


LESSON  XLV. 

1.  William  had   23   cents:    Thomas   gave   him  8  cents 
more,  George  6,  James  5,  and  David  7 ;  he  gave  15  cents 
for  a  book :  how  many  cents  had  he  left  ? 

2.  A  grocer  paid  $12  for  sugar,  $9  for  coffee,  $5  for  tea, 
$7  for  flour,  and  had  $10  left:  how  many  dollars  had  he 
at  first? 

3.  A  boy  has   11   cents:  his  father  gives  him  9  cents, 
his  mother  6,  and  his  sister  enough  more  to  make  34: 
how  many  cents  does  his  sister  give  him? 

4.  Five  men  bought  a  horse  for  $42:  the  first  gave  $13; 
the  second,  $7 ;  .the  third,  $5 ;   and   the  fourth,  $9 :    how 
many  dollars  did  the  fifth  give? 

5.  A  man  purchased  8  sheep,  at  $4  a  head;  5   barrels 
of  flour,  at  $3  a  barrel ;  4  yards  of  cloth,  at  $3  a  yard ; 
and  5  ounces  of  opium,  at  $1  an  ounce:  how  much  did 
he  spend? 

6.  A  boy  lost  25  cents :  after  finding  15  cents,  he  had 
25:  how  many  cents  had  he  at  first? 

7.  A  man  owed  a  debt  of  $28,  and  paid  all  but  $9 :  how 
much  did  he  pay? 

8.  Borrowed  $56 :  at  one  time  I  paid  $23 ;   at  another, 
V  all  but  $7 :  how  much  did  I  pay  the  last  time  ? 

9.  James  borrowed   37  cents :    at  one  time  he  paid    5 
cents,  at  another  8,  and  the  third  time,  all  but  15:   how 

many  cents  did  he  pay  the  third  time? 

(82) 


GENERAL  REVIEW.  83 

10.  A  farmer    sold    1    cow,  at   $18,  and    5   pigs,  at   $3 
each,  receiving  in  payment  3  sheep,  at  $3  each,  and  the 
rest  in  money:  how  much  money  did  he  receive? 

11.  A  farmer  sold  12  barrels  of  cider,  at  $3  a  barrel :  ho 
then  purchased  5  barrels  of  salt,  at  $3  a  barrel,  and  some 
sugar,  for  $8:  how  many  dollars  had  he  left? 

12.  A  merchant  purchased  13  hats,  at  $4  each;  5  pairs 
of  shoes,  at    $2    a   pair;  and    an    umbrella,  for  $7 :  what 
must  he  sell  the  whole  for  to  gain  $9? 

13.  If  2  barrels  of  flour  cost  $12,  what  will  7  barrels 
cost?     5  barrels? 

14.  If  3  barrels  of  cider  cost  $12,  what  will  4  barrels 
cost?    9  barrels? 

15.  If  4  yards  of  cloth  cost  $28,  what  will  7  yards  cost? 

16.  If  5  tons  of  hay  cost  $35,  what  will  8  tons  cost? 
If  7  apples  cost  28  cents,  what  will  3  apples  cost? 

18.  If  8  oranges  are  worth  24  apples,  how  many  apples 
are  3  oranges  worth? 

19.  If  2  pounds  of  cheese   cost   36  cents,  what   will  3 
pounds  cost? 

20.  If  8  yards  of  cloth  cost  $56,  what  will  7  yards  cost? 

21.  If  9  yards   of  calico   cost   72    cents,  what   will   6 
ards  cost?     8  yards?     10  yards? 

22.  A  walks  5   miles,  while  B  walks  3 :  when  A  has 
gone  35  miles,  how  far  has  B  gone? 

23.  Joseph  and  his  father  are  husking  corn :  the  father 
can  husk  7  rows  while  Joseph  husks  3 :  how  many  rows 
will  Joseph  husk  while  his  father  husks  42  ? 

24.  Charles   can    earn    $9   while    Mary  earns  $4:    how 
many  dollars  will  Charles  earn  while  Mary  earns  $28. 

25.  If  6  horses  eat  12  bushels  of  oats  in  a  week,  how 
many  bushels  will   10  horses  eat  in  the  same  time? 

26.  If  five  horses  eat  16  bushels  in  2  weeks,  how  long 
would  it  take  them  to  eat  56  bushels? 


* 


84        RAY'S   NEW   INTELLECTUAL  ARITHMETIC. 

27.  If  6  apples  arc  worth    18  cents,  how  many  apples 
must  be  given  for  5  oranges,  worth  6  cents  each? 

28.  How   many  horses   can    eat   in   9   days  the  same 
amount  of  hay  that  12  horses  eat  in  6  days? 


LESSON  XLVI. 

1.  If  4   yards   of  cloth    cost   $16,  what  will   5   yards 
cost?     9  yards? 

2.  What  are  f  of  72?    f  of  72? 

3.  If  you  had  64  cents,  how  many  oranges  could  you 
buy,  at  8  cents  each? 

4.  Ninety-six  is  how  many  times  6? 

5.  James  had  48  chestnuts:    he  gave  \  of  them  to  his 
brother,  and  J  to  his  sister:  how  many  had  he  left? 

6.  Nine  times  9  arc  how  many  times  12? 

7.  In  8f  how  many  ninths?     In  9^? 

8.  Keduee  ^\,  -ffo,  ||f,  to  their  lowest  terms. 

9.  Keduce  f,  T\,  3$,  to  a  least  common  denominator. 

10.  A    farmer    planted   4^  acres  in  potatoes,  20f  acres 
in  wheat,  and  24J  acres  in  oats:  how  many  acres  did  he 
plant  ? 

11.  From  9f  take  5f. 

12.  A  man   having  84  miles  to  travel,  went  J  of  the 
distance  the  first  day,  J   the  second,  and   the  rest   the 
third   day:    what  part  did   he  travel  the  last  day,  and 
how  far? 

13.  What  are  9  times  ^? 

14.  What  are  ^  of  12? 

15.  If  4  yards  of  cloth   cost   $15,  what  will   7  yards 
cost? 

16.  How  many  arc  7  times  7f  ? 

17.  Four  times  6f  are  how  many  times  7? 


GENERAL  REVIEW.  85 

18.  Bought  8J   pounds   of  sugar,   at  8  cents  a  pound, 
and  paid  for  it  with  milk,  at  5  cents  a  quart :  how  many 
quarts  did  it  take? 

19.  What  are  -f  of  }  of  |  of  6? 

20.  If  6  kegs  of  tar  cost  $1T%,  what  will  9  kegs  cost? 

21.  A  farmer  sold  a  horse  for  $99,  and  gained  |-  of  its 
cost:  what  did  it  cost? 

22.  If  -|  of  the  cost   of  a   horse  was   $96,  and  it  was 
paid  with  flour,  at   $6  a  barrel,  how   many   barrels   did 
it  take? 

23.  84  is  I  of  how  many  times  9? 

24.  -^  of  125  are  how  many  times  5? 

25.  f  of  81  are  f  of  what  number? 

26.  4.  of  35  are  f  of  how  many  times  f  of  16  ? 

27.  If  a  man  pays  $17^  for  4J  yards  of  cloth,  what  is 
the  cost  of  1  yard? 

28.  If  an  apple  is  worth  f  of  a  cent,  how  many  apples 
can  be  purchased  for  18  cents? 

29.  7f  are  £  of  what  number? 

30.  Bought    3^    dozen    hinges,   at   $14    a    dozen :    how 
much  did  they  cost? 

31.  Bought  30  yards  of  percale,  at  12^  Gents  a  yard: 
how  many  dollars  did  it  cost? 

32.  Paid    $7f   for   alpaca,   at   33J   cents  a  yard:    how 
many  yards  did  I  buy? 

33.  How  much  a  day  must  a  man  earn  to  receive  $72 
for  8  weeks,  6  days  to  the  week? 

34.  If  $2§  are  divided  equally  among  4  boys,  what  is 
each  boy's  share? 

35.  At  5  lemons   for   3   cents,  how    many  lemons   can 
be  bought  for  12  cents? 

36.  If  1J   yards    of  cloth   cost   $8,  how  much  can  be 
purchased  for  $12? 

37.  The  ago  of  Joseph  is  20   years,  which  is  f  of  the 


86        RAY'S   NEW   INTELLECTUAL   ARITHMETIC. 

age  of  his  father :  the  father's  age  is  10  times  that  of  his 
youngest  son :  what  is  the  age  of  the  father  ?  what  the 
age  of  the  youngest  son  ? 

38.  By  selling   a   quantity  of  cloth  for  $21,  I  made  f 
of  the  cost :    I   paid  for  it  with  corn,  at   $J  per  bushel  : 
how  many  bushels  did  I  give  ? 

39.  If  |  of  a  yard  of  cloth  cost  $f ,  what  will  3  yards 
cost? 

40.  What  will   be  the  cost  of  11  yards  of  cloth,   if  5£ 
yards  cost  $4f? 

41.  J  of  a   certain    number   is    2    more  than  J  of  12: 
what  is  the  number? 

42.  J    of  a    certain    number    is    3   less   than  -J-  of  30 : 
what  is  the  number? 

43.  |  of  20  are  6  less  than  how  many  thirds  of  21  ? 

44.  |  of  24  are  6  more  than  f  of  what  number? 

45.  ^  of  30,  increased  by  4,  are  1  less  than  J  of  some 
number :   what  is  the  number  ? 

46.  |  of  40  are  3  less  than  -f$  of  how  many  times  6  ? 

47.  A   boy   having   40    cents    gave    §   of  them   for   2 
melons :  what  was  the  price  of  1  melon  ? 

48.  James   had    14    cents,  and    gave  ^  of  them  to  his 
sister:  how  many  cents  had  he  left? 

49.  John  had  15  pears :  he  gave  J  to  Frank,  and  f  to 
Harry:  how  many  had  he  left? 

50.  A  man  had  30  yards  of  cloth,  and  sold  f  of  it  for 
$48 :  how  much  was  that  a  yard  ? 

51.  John  had  25  cents,  and  gave  f  of  them  for  peaches, 
at  2  cents  each :  how  many  did  he  buy  ? 

52.  A   boy  having    54    chestnuts,    divided    %   of  them 
among  3  girls :  how  many  did  each  receive  ? 

53.  A  man  had  28  barrels  of  flour,  and  sold  -f-  of  them 
for  $48:  what  was  that  a  barrel? 

54.  James  had  48  cents :  he  gave  f  to  his  brother,  and 


GENERAL  REVIEW.  87 

spent  the  rest  in  chestnuts,  at  9  cents  a  quart :  how  many 
quarts  of  chestnuts  did  he  buy? 

55.  Thomas  had  28  cents :  he  gave  J  to  his  sister,  and 
f  to  his    brother,   and   with   the  remainder  he  bought  3 
newspapers:  what  did  each  cost? 

56.  If  5  men   earn   $30  in   3   days,   how  much  will  2 
men   earn   in   the  same   time?    How  much  will  2  men 
earn  in  1  day? 

57.  6  is  what  part  of  f  of  40? 

58.  f  of  14  is  what  part  of  54? 

59.  |  of  12  is  what  part  of  |-  of  72? 

60.  £  of  20  is  what  part  of  twice  that  number  of  which 
14  is  |? 

Cl.  If  |  of  a  ton  of  hay  cost  $9,  what  will  £  of  a  ton 
cost? 

62.  If  $7    will   buy  56    yards   of  muslin,   how   many 
yards  will  $4  buy? 

63.  If  3  men  can  do  a  job  of  work  in  16  days,  in  how 
many  days  can  4  men  do  it? 

64.  If  3  men  spend   $12   in   1  week,  at  the  same  rate, 
how  many  dollars  would  2  men  spend  in  6  weeks? 

65.  If  6  men  do  a  piece  of  work  in   7   days,  in   how 
many  days  can  3  men  do  it? 

66.  If  5  men  do  a  piece  of  work  in    8    days,  in  how 
many  days  can  4  men  do  a  piece  twice  as  large? 

67.  If  6  men  perform  a  certain  amount  of  labor  in  5 
days,  in  how  many  days  can  2  men  do  J  that  amount? 

68.  James  had   16  apples :    he  kept  j-  of  them  himself 
and  divided  the  remainder  equally  among  3  of  his  com- 
panions: how  many  did  each  receive? 

69.  Three-fourths  of  24,  increased  by  §  of  12,  are  equal 
to  how  many? 

70.  Five-sixths  of  24,  diminished  by  £  of  20,  equal  how 
many  ? 


88        BAY'S    NEW  INTELLECTUAL  AKITHMETIC. 

71.  Two-thirds  of  12,  less  £  of  12,  arc  f  of  what  number? 

72.  Add  together  J,  §,  and  f  of  12. 

73.  From  10  take  f  of  itself;  add  to  the  remainder  its 
^ :  what  is  the  result  ? 

74.  Thomas  had  28  cents :  he  gave  fy  of  the  amount  to 
his  sister,  and  -|  of  the  remainder  to  his  brother :    how 
much  more  did  he  give  away  than  he  had  left? 

75.  James  had  35  marbles:    he  gave  to  Thomas  f  of 
them,  to  Charles  -| :  to  which  did  he  give  the  most,  and 
how  many?     What  number  had  he  left? 

76.  Thomas   had    $28:    he   kept  -f   of  the  whole,  and 
divided    the    remainder   equally  among    his   4    brothers : 
how  many  dollars  did  each  receive? 

77.  A  grocer  had  14  barrels  of  flour :  he  sold  ^  of  it  at 
$3   a   barrel,   and   the   remainder  at   $5   a   barrel :  what 
amount  did  he  receive? 

78.  Bought  15  yards  of  cloth,  at  $2  a    yard:  I   sold  J 
of  it  at  $4  a  yard,  f  at  $3  a  yard,  and  the  remainder  at 
$5  a  yard:   how  much  did  I  gain? 

79.  Bought  10  yards  of  cloth  for  $90,  and  sold  f  of  it  for 
$40 :  how  much  a  yard  did  I  gain  on  the  quantity  sold  ? 

80.  Two  men  travel  the  same  direction  :  A  is  40  miles 
ahead  of  B;    but  B  travels  23  miles   a    day,  and  A  18: 
in  how  many  days  will  B  overtake  A? 

81.  A  hare  is  90   yards   in   advance   of  a  hound:   the 
hound  goes  10  feet  in  a  second,  and  the  hare  7  feet  in  a 
second:    in   how  many  seconds  will  the  hound  overtake 
the  hare?     How  far  will  each  run? 

82.  If  a  hound   run  7  rods  while  a  hare  runs  4,  how 
far  will  the  hare  run  while  the  hound  runs  35  rods? 

83.  C  and  D  travel  in  the  same  direction :  C  is  15  miles 
ahead  of  D ;  but  D  travels  5  miles  an  hour,  and  C  only 
2 :  in  how  many  hours  will  D  overtake  C?     How  far  will 
D  have  traveled  ? 


GENEKAL  REVIEW.  89 

84.  A  cistern  containing  24  gallons,  is  filled  by  a  pipe 
at  the  rate  of  8  gallons  an  hour,  and  emptied  by  a  pipe 
at  the  rate  of  5  gallons  an  hour :  if  both  pipes  are  open, 
how  long  will  the  cistern  be  in  filling? 

85.  A  cistern  containing  36  gallons  has  2  pipes;  by  the 
first  it  receives  6  gallons  an  hour,  and  by  the  second  it 
discharges  9  gallons  an  hour :  if  both  pipes  are  left  open, 
how  long  will  it  take  to  empty  the  cistern? 

86.  A  pair  of  pants  cost  $8,  which  was  J-  of  the  cost  of 
a  coat ;  a  vest  cost  \  as  much  as  the  pants :  what  was  the 
cost  of  the  whole  suit? 

87.  Joseph    had    $1 :    he    spent    -|  of  the    amount    for 
oranges ;  %  of  the   remainder   for  lemons ;  and  -|-  of  the 
last  remainder    for  an  illustrated  paper:    how  much  had 
he  left? 

88.  When  hay  was  $20  a  ton,  I  gave  f  of  a  ton  for  4 
tons  of  coal :  what  was  the  coal  worth  per  ton  ? 

89.  A  man   can  perform  a  journey  in  3J  days :  what 
part  of  the  journey  can  he  perform  in  2J  days? 

90.  A   can    do  a    piece    of  work    in    2  days;    B,  in  4 
days;    and  C,  in  6  days:  in  what  time  will    they  all  do 
it  when  working  together? 

91.  Bought   20    yards    of  cloth,  at   $4   a  yard,  and  15 
yards,  at  $3  a  yard :  sold  -£  of  the  whole,  at  $3  a  yard, 
and  the   remainder,   at  $4  a  yard :    what   was  the  entire 
loss?     What  the  average  loss  per  yard? 

92.  William   had  $96.     He    spent   ^  for  books,  -fr  of 
the  remainder  for  clothing,  -J  of  what  then  remained  for 
furniture,  and,  with  what  was   left,  bought  wheat,  at  $1 
a  bushel  :    how  many  bushels  did  he  buy? 

93.  A  and    B   are    traveling   in  the   same  direction,  A 
being  36  miles  ahead  of  B ;    A  travels  |  of  the  distance 
per  hour  that  B  travels,  and  B  travels  6  miles  an  hour: 
in  how  many  hours  will  B  overtake  A? 


LESSON  XL VII. 


UNITED   STATES    MONEY. 


10  mills,  marked  m.,  arc  1  cent,  marked  ct. 

10  cents,  "  1  dime,  "         d. 

10  dimes  or  100  cents  "  1  dollar,  "         $. 

10  dollars  "  1  eagle,  "         E. 

1.  How  many  mills  in  2  cents? 

SOLUTION. — In  1  cent  there  are  10  mills;  then,  in  2  cents  there  are 
2  times  10  mills  =  20  mills. 

2.  How  many  mills  in  3  cents?     In  4  cents?     5  cents? 
6  cents?     7  cents?     8  cents?     9  cents? 

3.  How    many    cents    in    2    dimes?      In    3    dimes?     4 
dimes     5?     6?     7?    8?     9? 

4.  How   many  dimes   in   2   dollars?     In   3  dollars?    4 
dollars?     5?     6?     7?     8?     9? 

5.  How   many  dollars    in  2   eagles?     In   3   eagles?     4 
eagles?     5?     6?     7?     8?    9? 

G.  How  many  cents  in  2  dollars? 

SOLUTION. — In  1  dollar  there  are  10  dimes;  then,  in  2  dollars  there 
are  2  times  10  dimes  =  20  dimes.  In  1  dime  there  are  10  cents; 
then,  in  20  dimes  there  are  20  times  10  cents  =  200  cents. 

7.  How    many   cents   in   3   dollars?     In   4  dollars?     5 

dollars?     6?     7?     8?     9? 
(90) 


TABLES.  91 

8.  Twenty  cents  are  how  many  dimes? 

SOLUTION. — 10  cents  are  1  dime;  then,  20  cents  are  as  many  dimes 
as  10  is  contained  times  in  20,  which  are  2. 

9.  Thirty  cents  are  how  many  dimes?     40  cents?     50? 
60?     70?     80?     90? 

10.  Twenty  dimes  are  how  many  dollars?     30  dimes? 
40?     50?     60?     70?     80?     90? 

11.  Two  hundred  cents  are  how  many  dollars? 

SOLUTION. — 10  cents  are  1  dime;  then,  200  cents  are  as  many 
dimes  as  10  is  contained  times  in  200,  which  are  20.  10  dimes  are  1 
dollar;  then,  20  dimes  are  as  many  dollars  as  10  is  contained  times 
in  20,  which  are  2. 

12.  Three   hundred   cents  are  how  many  dollars?    400 
cents?     500?     600?     700?     800?     900? 


LESSON  XL VIII. 

DRY    MEASURE. 

2  pints  (pt.)         are  1  quart,        marked    qt. 
8  quarts  "    1  peck,  "       pk. 

4  pecks  "    1  bushel,  "       bu. 

1.  How    many  pints    in    2    quarts?     In    3    quarts?     4 
quarts?     5?     6?     7? 

2.  How  many  quarts  in  2  pecks?     In  3  pecks? 

3.  How  many  pecks  in  2  bushels?     In    3  bushels?     4 
bushels?     5?     6?     7?    8?     9?     10?     11?     12? 

4.  Four  pints   are   how  many  quarts?      6   pints?      8? 
10?     12?     14? 

5.  Sixteen  quarts  are  how  many  pecks  ?     24  quarts  ? 

6.  Eight   pecks    are    how  many  bushels?     12    pecks? 
16?     20?     24?     28? 


92         KAY'S  NEW  INTELLECTUAL  ARITHMETIC. 

1 

7.  Reduce  3  qt.  1  pt.  to  pints. 

SOLUTION.— In   1   qt.  there  are  2  pt.;  then,  in  3  qt.  there  are  3 
times  2  pt.  =  6  pt.;  6  pt  -f-  1  pt.  =  7  pt. 

8.  Eeduce  3  pk.  5  qt.  to  quarts. 

9.  Eeduce  3  bu.  2  pk    to  pecks. 

10.  Reduce  2  pk.  3  qt.  1  pt.  to  pints. 

11.  Reduce  2  bu.  3  pk.  7  qt.  to  quarts. 

12.  Reduce  1   bu.  2  pk.  2  qt.   1  pt.  to  pints. 

13.  Reduce  7  pt.  to  quarts. 

SOLUTION. — 2  pt.  are  1   qt.;  then,  7  pints  are  as  many  quarts  as  2 
is  contained  times  in  7,  which  are  3  and  1  rem.  =  3  qt.  1  pt. 

14.  Reduce  9  pt.  to  quarts.     11  pt.     13.     15. 

15.  Reduce  10   qt.   to    pecks.     11    qt.      12.      13.      17. 
19.     23.     27. 

16.  Reduce  7    pk.  to    bushels.      10    pk.     13.     15.     17. 
23. 

17.  Reduce  27  pt.  to  pecks. 

SOLUTION.— 27  pt.  =  13  qt.  1  pt.;  13  qt.  =  1  pk.  5  qt.:  therefore,  27 
pt.  =  1  pk.  5  qt.  1  pt. 

18.  Reduce  35  pt.  to  pecks.     39  pt.     43.     45. 

19.  Reduce  53  qt.  to  bushels.     55  qt.     57.     59. 

20.  Reduce  83  qt.  to  bushels.     86  qt.     89.     92. 

21.  Reduce  223  pt.  to  bushels.     224  pt.     226.     228. 

22.  Reduce  345  pt.  to  bushels.     346  pt.     347.     348. 

23.  Reduce  6  bu.  2  qt.  to  quarts. 

24.  Reduce  2  bu.  1  pt.  to  pints. 

25.  Reduce  4  bu.  2  pk.  to  pints. 

26.  Reduce  3  bu.  7  qt.  1  pt.  to  pints. 

27.  Reduce  5  bu.  3  pk.  1  pt.  to  pints. 

28.  Reduce  7  bu.  3  pk.  7  qt.  to  pints. 


TABLES. 

LESSON  XLIX. 
LIQUID    MEASURE. 

4  gills  (gi.)     are  1  pint,      marked     pt. 
2  pints  "     1  quart,          "          qt 

4  quarts  "     1  gallon,         "        gal. 

1.  How  many  pints  in  2  qt?     In  3  qt? 

2.  How  many  quarts  in  2  gal.?     In    3    gal.?     4   gal.? 
5?     6?     7?     8?     9?     10?     11?     12? 

3.  5  gi.  are  how  many  pints?     6  gi.?     7? 

4.  3  pt.  are  how  many  quarts?     4pt?     5?     6?     7? 

5.  5  qt  are  how  many  gallons?     6qt?     7?      8?    9? 
10?     11?     12? 

6.  How  many  gills  in  1  qt?     In  2  qt?     3  qt? 

7.  How  many  pints   in  1   gal.  ?      In  2  gal.  ?      3    gal.  ? 
4?     5? 

8.  How  many  gills   in    1    gal.?    In   2   gal.?     3   gal.? 
4?    5? 

9.  Reduce  1  pt  3  gi.  to  gills. 

10.  Reduce  3  qt.  1  pt  to  pints. 

11.  Reduce  5  gal.  2  qt.  to  quarts. 

12.  Reduce  2  qt  1  pt.  1  gi.  to  gills. 

13.  Reduce  4  gal.  3  qt.  1  pt  to  pints. 

14.  Reduce  1  gal.  1  qt.  1  pt.  3  gi.  to  gills. 

15.  Reduce  13  gi.  to  quarts. 

16.  Reduce  23  pt  to  gallons. 

17.  Reduce  79  gi.  to  gallons. 

18.  Reduce  97  gi.  to  gallons.     98.     100.     102. 

19.  Reduce  187  gi.  to  gallons.     188.     190.     192. 

20.  Reduce  6  gal.  2  pt  to  gills. 

21.  Reduce  8  gal.  3  gi.  to  gills. 

22.  Reduce  10  gal.  10  qt  10  pt.  to  gills. 


94        KAY'S    NEW  INTELLECTUAL  ARITHMETIC. 


LESSON    L. 
AVOIRDUPOIS   WEIGHT. 

16  drams  (dr.)  are  1  ounce,  marked  oz. 

1G  ounces  "  1  pound,  "  Ib. 

100  pounds  "  1  hundred-weight,         "  cwt. 

20  hundred-weights    «  1  ton,  «  T. 

1.  How   many   drams    in    2    oz. ?     In    3    oz. ?     4    oz.? 
5?     6? 

2.  How  many  ounces  in  2  Ib.  ?     In  3  Ib.?     4   Ib.?     5? 
6?     10? 

3.  How  many  pounds  in  2  cwt.?     In  3  cwt.?     4  cwt.? 
5?     6?     7?     8?     9? 

4.  How  many  hundred-weights  in  2  tons?     In  3  tons? 
4  tons?     5?     6? 

5.  Twenty  dr.  are  how  many  ounces?     27  dr.?     35? 

6.  Forty-two  oz.  are  how  many  pounds  ?     53  oz.  ?     75  ? 
90? 

7.  Three  hundred  Ib.  are  how  many  hundred- weights? 
450  Ib.?     575?     1200? 

8.  Forty  cwt.   are    how   many   tons?      50    cwt.?     75? 
80?     96? 

9.  How  many  ounces  in  \  Ib.  ? 

SOLUTION. — In  1  Ib.  there  are  16  oz.;  then,  in  \  Ib.  there  are  \  of 
16  =  8  oz. 

10.  How  many  ounces  in  \  Ib.  ?    f  Ib.  ? 

11.  How   many  pounds   in  \  cwt.?     In  J  cwt.?     In  j 
cwt.?     £?     |?     f?     f? 

12.  Reduce  4  oz.  11  dr.  to  drams. 

13.  Reduce  10  Ib.  10  oz.  11  dr.  to  drams. 

14.  Reduce  15  cwt.  45  Ib.  to  pounds. 


TABLES.  95 

15.  Reduce  4  T.  10  cwt.  75  Ib.  to  pounds. 

16.  Twelve  ounces  arc  what  part  of  a  pound? 

SOLUTION.  —  In  1  Ib.  there  are  16  oz.;  then,  12  oz.  are  |f  —  f  H>. 

17.  Eight  oz.  are  what  part  of  a  pound?     10  oz.?     14? 

18.  Ten   Ib.  are  what  part  of  a    hundred-weight?     20 
Ib.?    25?    40?    50?     60?    75?     80? 

19.  Four  cwt.  are  what  part  of  a  ton?    5   cwt.?     6? 
8?     10?     12?     15?     16?     18? 

LESSON  LI. 

LONG   MEASURE. 


12 

inches  (in.) 

are 

1 

foot, 

marked 

ft. 

3 

feet 

n 

1 

yard, 

n 

yd. 

5J 

yards 

u 

1 

rod, 

« 

rd. 

40 

rods 

u 

1 

furlong, 

u 

fur. 

8 

furlongs 

ii 

1 

mile, 

u 

mi. 

1.  How  many  inches  in  2  ft.  ? 

2.  How  many  feet  in  2  yd.?     In  3  yd.?     4  yd.?     5? 

3.  How  many  yards  in  2  rd.?     In  4  rd.?     5  rd.?     7? 
10? 

4.  How  many  rods  in  3  fur.?     In  4  fur.?     5  fur.?     6? 
7?     9? 

5.  How  many  furlongs  in   9  miles? 

6.  Thirty-six  in.  are  how  many  feet?     48  in.? 

7.  Fifteen  ft,  arc  how  many  yards?     21  ft? 

8.  Twenty  -two  yd.  arc  how  many  rods?     33  yd.? 

9.  Six  hundred  and  forty  rd.  are  how  many  miles? 

10.  What  is  the  value  of  £  yd.? 

SOLUTION.—  In  1  yd.  there  are  3  ft.;  then,  in  f  yd.  there  are  f  of 
3  ft.  =  Yi  or  2£  ft.  In  1  ft.  there  are  12  in.;  then,  in  £  ft.  there  are 
g  of  12  in.  =  6  in.;  therefore,  £  yd.  =  2  ft.  0  in. 


96 


KAY'S  NEW  INTELLECTUAL  ARITHMETIC. 


11.  What  is  the  value  of  §  ft.?     |  ft.? 

12.  What  is  the  value  of  §  yd.?     f  yd.? 

13.  What  is  the  value  of  T6T  rd.?    J  rd.  ? 

14.  What  is  the  value  of  J-  mi.  ?    J  mi.  ? 

15.  Sixteen  rd.  arc  what  part  of  a  mile? 


i? 


f?  i 


SOLUTION. — In  1  mi.  there  arc  8  fur.;  in  8  fur.  there  are  320  rd.; 
then,  16  rd.  are  •£&  =  fa  of  a  mile. 

16.  Twenty-four  rd.  are  what  part  of  a  mile? 

17.  Three  yd.  are  what  part  of  a  rod? 

18.  Two  ft.  are  what  part  of  a  yard?     Of  a  rod? 

19.  Six  in.  are  what  part  of  a  foot?     Of  a  yard?     Of 
a  rod? 

LESSON  LII. 


TIME   TABLE. 


60  seconds  (sec.) 
60  minutes 
24  hours 

365  days 

366  days 
100  years 

7  days 
4  weeks 
12  calendar  months 


are 

1 

minute,              marked  min. 

u 

1 

hour, 

a 

hr. 

u 

1 

day, 

a 

da. 

It 

1 

common  year, 

u 

c.  yr. 

a 

1 

leap-year, 

u 

l.yr. 

« 

1 

century, 

u 

cen. 

n 

1 

week, 

u 

wk. 

n 

1 

month, 

u 

mon. 

a 

1 

year, 

u 

y*« 

One  solar  year  contains  365  days,  5  hours,  48  minutes, 
and  46  seconds,  or  365J  days,  nearly. 

The  following  table  shows  the  names  of  the  different 
months  of  the  year,  and  the  number  of  days  embraced 
in  each : 


TABLES.  97 

January,  1st  month,  31  days. 

February,  2d  «        28  or  29  « 

March,  3d  "  31  « 

April,  4th  «  30  " 

May,  5th  «  31  « 

June,  6th  "  30  " 

July,  7th  "  31  " 

August,  8th  "  31  " 

September,  9th  "  30  " 

October,  10th  "  31  " 

November,  llth  «  30  « 

December,  12th  "  31  " 

The   names  of  the   months   which   have  30  days  each 
may  be  remembered  by  the  following  couplet: 

Thirty  days  have  September, 
April,  June,  and  November. 

1.  What  is  the  value  of  1  min.?     |  min.?    f?    f? 

2.  What  is  the  value  of  £  hr.?      f    hr.?     f?     f?     J? 

I?    V 

3.  What  is  the  value  of  £  da.?     f   da.?    f?    ^?    f? 

A? 

4.  What  is  the  value  of  f-  wk.  ?     f  wk.  ? 

5.  What  is  the  value  of  £  mon.?     f   mon.?     f?    £? 
ft?    if? 

6.  Twenty  sec.  are  what  part  of  a  minute? 

7.  Fifty  min.  are  what  part  of  an  hour? 

8.  Twelve  hr.  are  what  part  of  a  day?     Of  a  week? 

9.  Five  days  are  what  part  of  a  week  ? 

10.  Eight  calendar  months  are  what  part  of  a  year? 

11.  Three  hr.  30  min.  are  what  part  of  a  day? 

12.  Three  da.  12  hr.  are  what  part  of  a  week? 

13.  One  wk.  3  da.  are  what  part  of  a  month? 

Int.  7. 


98       RAY'S   NEW  INTELLECTUAL  ARITHMETIC. 

14.  One  wk.  3  da.  16  hr.  are  what  part  of  a  month  ? 

15.  How    many   days    in    April    and    May  taken    to- 
gether? 

16.  How  many  days  in  June,  July,  and  August  taken 
together  ? 

17.  How  many  days   in   September,  October,  and  No- 
vember taken  together? 

18.  How  many  days  from  July  12  to  July  28? 

19.  How   many    days  from   October    27    to  December 
25? 

20.  How  many  days  from  the  Vernal  Equinox,  March 

20,  to  the  Autumnal  Equinox,  September  22? 

21.  How  many  days   from   the  Summer  Solstice,  June 

21,  to  the  Winter  Solstice,  December  21? 


LESSON  LIIL 

1.  What   is   the   cost   of  5   bu.  3   pk.   of  corn,   at   60 
cents  a  bushel? 

2.  When  milk  is  5  cents  a  pint,  what  does  a  milkman 
get  for  4  gal.  2  qt.  1  pt? 

3.  At   10   cents   a   pound,  what   will   be  the  cost  of  7 
Ib.  12  oz.  sugar? 

4.  What    will   it   cost   to   build   a   fence  5  rd.  2  yd.  2 
ft.  3  in.  long,  at  $12  a  rod? 

5.  A  steamer  from  Milwaukee  to  Grand  Haven,  at  the 
average  rate  of  9    miles  an  hour,  was  9  hr.  26    min.  40 
sec.  in  making  the  trip:  what  is  the  distance? 


GENERAL  REVIEW.  99 

6.  How  much  wine,  at   $8  a  gallon,  can  be  purchased 
for  $23? 

7.  How  much  coffee,  at  30  cts.  per  lb.,  can  be  bought 
for  $5? 

8.  Add  T3g.  da.  and  f  hr. 

9.  Add  |  rd.,  J  yd.,  and  f  ft. 

10.  From  f  bu.,  take  f  pk. 

11.  If  1  bu.  3  pk.  of  oats   are  worth  70  ct.,  what   are 
2  bu.  1  pk.  4  qt.  worth. 

12.  If  a    wagon-wheel    go    3   yd.    1    ft.   in    making    1 
revolution :    how    far    will    it   go    in    making    7    revolu- 
tions ? 

13.  If  f   T.   of    hay  cost   $8,  what   will  3  cwt.  75  lb. 
cost? 

14.  The   time   by   rail   from   Cincinnati   to   Dayton,  a 
distance   of  60  miles,  is    2  hr.  24  min.,  what  is  the  rate 
of  travel  per  hour  of  the  train  ? 

15.  If  a  cart-wheel  make  1  revolution  in  going  3  yd. 
1  ft.  6  in.,  how  many  revolutions  will  it  make  in  going 
1  rd.  5  yd.? 

16.  How  many  weeks  in  April,  May,  and  June   taken 
together  ? 

17.  I  bought   some  roasted  Java    coffee   for  $2  and  35 
ct.,  paying   40   ct.  a   lb. :    how   many  lb.  and   oz.  did   I 
buy? 

18.  If  there  are  3  gal.  in  a  dozen  bottles  of  wine,  how 
much  will  3  dozen  bottles  cost,  at  50  ct.  a  quart? 

19.  If  2   bu.  3    pk.  of  corn    cost   $1  and  65  ct. :   how 
much  is  that  a  bushel? 

20.  If  there  are  25    bu.  in    a   ton    of  coal,  how  much 
will    150   bu.  cost,  at    $3  and  75  ct.  a  ton?     How  much 
a  bushel? 

21.  A  lot  is  50  ft.  wide,  and    100  ft.  long:    how  much 
will  it  cost  to  put  a  fence  around  it,  at  $5  a  rod? 


100       RAY'S  NEW  INTELLECTUAL  ARITHMETIC. 

LESSON  LIV. 

1.  A  merchant   bought  at  one  time  33  gallons  of  oil ; 
at  another,  20   gallons ;    at  another,  50 ;    and  at  another, 
62:  how  many  gallons  did  he  buy  in  all? 

2.  A  lady  paid  $23  for  a  dress,  $18  for  a  shawl,  and  $9 
for  a  bonnet :  what  did  she  pay  for  all  ? 

3.  I  owe  A  $50,  B  $75,  C  $40,  and  D  $20 :  how  much 
money  do  I  owe  altogether? 

4.  Having  $92,  I  purchased  a  watch  for  $73 :  how  much 
money  had  I  left  ? 

5.  A  man  bought  a  horse  for  $110,  and  sold  him  for 
$145 :  how  much  did  he  make  ? 

6.  George    bought    candles    for    25  ct,  soap  for  10  ct., 
sugar  for  35   ct.,   and   starch  for    3   ct. ;    he    gave    the 
grocer  $1,  and  received  30   ct.  change :  how    much  was 
this  incorrect? 

7.  A   bo}r  had  $5,  from  which  he  took  at  one  time  $1 
and  50  ct.;  at  another,  40  ct.;   at  another,  $1  and  10  ct. : 
how  much  money  had  he  left? 

8.  What  will  be  the  cost  of  5  yd.   of  cloth,  at  $2  and 
50  ct.  a  yard? 

9.  A  man   traveling  at  the   rate  of  5   miles   an  hour, 
meets    a    stage    going    at   the    rate   of  9  miles  an  hour: 
how  far  apart  will  they  be  in  10  hours? 

10.  Bought   15  Ib.    of    sugar,  at   11  ct.    a   pound,  and 
13  Ib.,  at  9  ct.  a  pound,  what  did  the  whole  cost? 

11.  Henry  has    19  ct.,  George  3  times  as   many,  lack- 
ing 10  ct. :  how  many  have  both? 

12.  How  many  yards  in  3  bales  of  cloth,  each  contain- 
ing 5  pieces,  of  40  yd.  each  ? 

13.  If  a  boat  sail  48  miles  in  12  hours,  how  far  will  it 
sail  in  7  hours? 


GENERAL   11EVIEW.  101 

14.  At  15  ct.  a  pound,  how  many  pounds  of  beef  can 
be  purchased  for  $6. 

15.  Three  men  bought  a  horse   for  $90 ;   after  keeping 
him  6  weeks,  at    $3  a  week,   and  the  use    of  him  being 
worth  $42,  they  sold   him   for  $99 :    what  did  each  man 
make  ? 

16.  A  farmer  sold  12  bu.  of  corn,  at  45  ct.,  and  8  bu.  of 
wheat,  at  95  ct.  a  bushel ;  he  then  bought  7  yd.  of  cloth, 
at  80  ct.  a  yard,  and  spent  the  balance  for  coffee,  at  33J 
ct.  a  pound :    how  much  coffee  did  he  buy  ? 

17.  If  I  buy  9  bbl.   of  flour,  at  $6.50  a  barrel,  and  12 
Ib.  of  sugar,  at  12^  ct.  a  pound :  how  many  apples,  at  60 
ct.  a  bushel,  will  I  have  to  sell  to  pay  for  them  ? 


LESSON  LV. 

1.  If  J  of  a  yd.  of  cloth  cost  $2,  what  will  J  of  a  yd.  cost? 

2.  Iff  of  a  yd.  of  cloth  cost  $5,  what  will  f  of  a  yd.  cost? 

SOLUTION.— The  cost  of  £  of  a  yard  will  be  £  of  $5  =  $f;and  a 
yard  will  cost  3  times  $f  =  $-L5-:  then,  \  of  a  yard  will  cost  \  of  $-\& 
=  I-1/-;  and  |  of  a  yard  will  cost  3  times  $\5-  ==  $5|. 

3.  If  I  of  a  bbl.  of  flour  cost  $3,  what  will  f  of  a  bbl. 
cost? 

4.  If  *  of  a  yd.  of  flannel  cost  24  cts.,  what  will  ^  of 
a  yd.  cost? 

5.  If  |  of  a  ton  of  hay  cost  $15,  what  will  one-half  a 
ton  cost? 

6.  If  |  of  an  orchard  contain  30  fruit  trees,  how  many 
trees  are  there  in  -£•$  of  it? 

7.  If  If  yd.  of  cloth  cost  $14,  what  will  2|  yd.  cost? 

8.  If  11  bbl.  of  flour  cost  $5J,  what  will  2£  bbl.  cost? 

9.  If  3|  Ib.  of  cheese  cost  60  ct.,  what  will  2f  Ib.  cost? 


102       RAY'S  NEW  INTELLECTUAL  ARITHMETIC. 

10.  A  traveled  30  mi.  in  3|  hr. :  at  that  rate,  how  far 
could  he  travel  in  7-J  hr.  ? 

11.  If  a   man    earn    $1J   in  10  hr.,  how  much  can  he 
earn  in  11  hr.  ? 

12.  A  can  earn  $9|  in  6  da.,  of  8  hr.  each :  how  much 
can  he  earn  in  7  da.,  of  9  hr.  each? 

13.  If  5f  bu.  of  wheat  cost  $9£,  what  will  3J  bu.  cost? 

14.  If  8£  is  f  of  a  number,  what  is  4  of  it? 

15.  If  3J  is  2J  times   some    number,  what  is  2J  times 
that  number? 

16.  If  |  of  a  barrel  of  flour  cost  84J,  what  will  f  of  a 
barrel  cost? 

17.  If  |   of  a   yard   of  lace  cost  $f ,  what  will  f  of  a 
yard  cost? 

18.  Two-thirds  of  1J  are  -f-  of  what  number? 

19.  Five-ninths  of  5J  are    -|    of  what  number? 

20.  Four-sevenths  of  4f  are  T5T  of  what  number? 

21.  Five-sevenths  of  5|  are  -^  of  what  number? 

22.  Two-thirds  of  2f  are  -|-    of  how  many  times  2  ? 

23.  Three-fifths  of  1J  are  -f-  of  how  many  times  4? 

24.  Three-fourths  of  3^  are  f  of  how  many  times  3? 

25.  John  has  10  marbles,  and  £  of  what  John  has  are 
•fj-  of  what  James  has :  how  many  has  James  ? 

26.  Jane  received  ^  of  60  plums;  she  gave  away  $  of 
f  of  them :  how  many  were  left  ? 

27.  James  has  a  given   distance  to  travel;   after  going 
35    mi.,    there    remain  ^  of    the   distance:    when  he  has 
gone  f  of  the  remainder,  how  far  must  he  then  go? 

28.  A  horse   cost  $40;  f  of  the  price  of  the  horse  =  £ 
of  the  price  of  a  cart:  what  did  the  cart  cost? 

29.  B's  coat  cost  $27,  and  his  hat  $8 ;  f  of  the  cost  of 
the  coat  -f-  f  that  of  the  hat  =  f  of  the  cost  of  his  watch  : 
what  did  the  watch  cost? 

30.  Mary  lost  f   of  her  plums ;    she  gave  |  of  the  re- 


GENERAL  REVIEW.  103 

maindcr  to  Sarah,  and  had  6  plums  left:  how  many  had 
she  at  first? 

31.  John   has  12   cents;    f  of   his  money  —  £  of  f  of 
William's  money:  how  much  has  William? 

32.  On  counting  their  money,  it  was  found  that  A  had 
12  cents  more  than  B ;    and  that  ^  of  B's  money  =  |-  of 
A's :  how  much  had  each  ? 

33.  In  an  orchard,  J   are  apple-trees,  \  are  pear-trees, 
-jJj  are  plum-trees,  and  the  remainder,  which  is  32,  cherry- 
trees  :  how  many  trees  are  there  of  each  kind  ? 

34.  In  an  orchard  of  apple   and  pear-trees,  the  latter 
are  -f  of  the  whole ;  the  apple-trees  are  25  more  than  the 
pear-trees :  how  many  are  there  of  each  ? 

LESSON  LVI. 

1.  What  number  added  to  itself  will  give  a  sum  equal 
to  14? 

SOLUTION. — A  number  added  to  itself  is  twice  the  number;  then, 
twice  the  number  is  14;  and  the  number  is  \  of  14=  7. 

2.  What  number  added  to  itself  3  times  will  make  32  ? 

3.  Divide  16  in  two  parts,  so  that  the  second  part  shall 
be  3  times  the  first. 

4.  Divide  48  into  two  such  parts,  that  the  second  shall 
be  7  times  the  first. 

5.  Divide  24  into  three  parts,  so  that  the  second  shall 
be  2  times  and  the  third  3  times  the  first. 

6.  Divide  45  into  three  parts,  so  that  the  second  shall 
be  three  times  and  the  third  5  times  the  first? 

7.  When    10   was   taken    from  a    number,  f   of  it   re- 
mained:  what  was  the  number? 

8.  The  sum  of  two  numbers  is   25 ;  if  10  is   the   less 
number,  what  is  their  difference? 


104      RAY'S   NEW  INTELLECTUAL  ARITHMETIC. 

9.  The  sum  of  two  numbers  is  12 ;  if  6  be  added  to 
the  sum,  the  result  will  be  twice  the  greater  number; 
what  are  the  numbers? 

10.  If  6  be  taken  from  the  difference  of  two  numbers, 
the  remainder   will   be    2;    if  4  is   one  of  the  numbers, 
what  is  the  other? 

11.  If  10  be  added  to   the  difference  of  two  numbers, 
the  sum  will   be   6   more  than  the  greater  number,  which 
is  19:  what  is  the  less  number? 

12.  If  10  be  taken  from  the  sum  of  two  numbers,  8  will 
be  left ;  if  5  is  one  of  the  numbers,  what  is  the  other  ? 

13.  The  sum  of  two  numbers  is  16,  and  their  difference 
4:  what  are  the  numbers? 

SOLUTION. — Twice  the  greater  number  is  16  -f-  4  =  20;   then,  the 
greater  number  is  £  of  20  =  10,  and  the  less  number  is  10  —  4  =  6. 

14.  The  sum  of  two  numbers  is  25.  and  their  difference 
5  :  what  are  the  numbers  ? 

15.  The  sum  of  two  numbers  is  31,  and  the  greater  ex- 
ceeds the  less  by  7 :  what  are  the  numbers  ? 

16.  Divide   15  cents  between  A  and  B,  so   that  B  ma^ 
have  3  cents  more  than  A. 

17.  Thomas   has   5   apples   more  than  James,  and  both 
together  have  19:  how  many  has  each? 

18.  Thomas  and  James  each  had  the  same  number  of 
cents,  when    Thomas   found  8  more;    they  then  had  to- 
gether 32  cents :  how  many  had  each  ? 

19.  Thomas  and  William  each  bought  the   same  num- 
ber  of   peaches;    after   Thomas    ate    4,   and    William  6, 
they  both  together  had  20  left :    how  many  peaches  had 
each  remaining? 

20.  Mary  bought  twice  as  many  cherries  as  Sarah ;  and, 
after  Mary  ate  7,  and  Sarah   5,  they  had  only  24  left: 
how  many  had  each  left? 


GENERAL  KEVIEW.  105 

21.  If  5  bo  added  to   three   times    a   certain    number, 
the  sum  will  be  50:  what  is  the  number? 

22.  If  f  of  a  certain    number  be   increased  by  10,  the 
sum  will  be  31:  what  is  the  number? 

23.  If  i  of  a  number  be  diminished  by  7,  the  remain- 
der will  be  21:  what  is  the  number? 

24.  James  is  4  years  older  than  Henry,  and  Henry  is 
3  years  younger  than  Oliver;   the  sum  of  all  their  ages 
is  37  years :  what  is  the  age  of  each  ? 

SOLUTION. — 3  times  Henry's  age  is  37  yr.  —  4  yr.  —  3  yr.  =  30 
yr.;  then,  Henry's  age  is  £  of  30  yr.  =  10  yr.,  James'  age  is  10 
yr.  -{-  4  yr.  =  14  yr.,  and  Oliver's  age  10  yr.  -J-  3  yr.  =  13  yr. 

25.  Mary  has  8  cts.  more  than  Jane,  and  Sarah  3  less 
than  Mary;  they  all  have  43  ct. :  how  many  has  each? 

26.  The  sum  of  the  ages  of  Mary  and  Frank  is  42  years ; 
Mary  is  twice  as  old  as  Frank,  less  3  years :  what  is  the 
age  of  each? 

27.  I  bought  a  watch,  a  chain,  and  a  ring,  for  $62 ;  the 
chain  cost  $5  less  than  the  ring,  and  the  watch  $12  more 
than  the  chain :  what  did  I  pay  for  each  ? 

28.  Thirty  cents   are  6  cents   less  than   1  of  $  of  my 
money :  how  much  have  I  ? 

29.  John  has  twice  as  much    money  as   James,  -f-  $3 ; 
Frank  has  as  much  as  John  and  James,  -j-  $7 ;  together 
they  have  $55 :  how  much  has  each  ? 

30.  Joseph  has  3  times  as  much  money  as  Thomas — $2 ; 
Paul  has  twice  as  much  as  Joseph  and  Thomas  together 
— $20 ;  together  they  have  $22 :  how  much  has  each  ? 

31.  A  horse,  buggy,  and  harness  cost  $225;  the  horse 
cost    $50   more    than   the   harness,    and    the    buggy   $25 
more   than   the   horse   and  harness  together :    what  was 
the  cost  of  each  ? 


106      KAY'S    NEW   INTELLECTUAL  ARITHMETIC. 

LESSON  LVIL 

1.  Divide  15  into  two  parts,  so  that  the  less  part  may 
be  f  of  the  greater. 

SOLUTION.  f  -j-  f  =  f  j  f  of  the  greater  part  =  15:  then,  £  of  the 
greater  part  is  |-  of  15  =  3,  and  the  greater  part  is  3  times  3  =  9;  the 
less  part  is  15  —  9  =  6. 

2.  Thomas  and  John  have  $60  to  pay ;  John  has  f  as 
much  to  pay  as  Thomas :  what  must  each  pay  ? 

3.  I  had  56  mi.  to   travel   in  2    da. ;    the  second  da.  I 
went  f  as  far  as  the  first:  how  far  did  I  travel  each  da.? 

4.  Divide  100  into  two  such    parts,  that  |-  of  the  first 
less  8  will  equal  the  second. 

5.  Divide  the  number  45  into  three  such  parts,  that  the 
second  shall  be  |-,  and  the  third  J  of  the  first  part. 

6.  A,  B,  and  C,  together  have  40  ct. ;   B  has  f  as  many 
as  A,  and  C  f  as  many  as  B:   how  many  cents  has  each? 

SOLUTION.  C  has  f  of  |-  =  -f  as  many  as  A;  then,  |  -f  f  -f-  f  = 
-J50-;  and  -^,  or  twice  as  many  as  A,  =  40  ct.  Then,  A  has  \  of  40 
ct.  =  20  ct.,  B  has  f  of  20  ct.  —  12  ct.,  and  C  has  f  of  20  ct.  =  8  ct. 

7.  A  tree   70   ft.  long   was   broken   into  3  pieces;   the 
middle  part  was  f  of  the  top  part;    the  lower  part  was 
f  of  the  middle  part:  what  was  the  length  of  each? 

8.  I  bought  a  hat,  coat,  and  vest,  for  $34;  the  hat  cost 
|  of  the  price  of  the  coat,  and  the  vest  f  the  price  of  the 
hat :  what  was  the  cost  of  each  ? 

9.  Divide  38    ct.  between  A  and  B,  so   that   f  of  A's 
share  may  be  equal  to  f  of  B's. 

SOLUTION.  \  of  A's  share  is  \  of  f  =  T%  of  B's,  and  A's  share  is  3 
times  fSo=T9o  of  B's;  then,  fg  -f-  T9^  =  |f  of  B's  share,  or  38  ct. 
y1^  of  B's  share  is  ^  of  38  ct.  =  2  ct.,  and  B's  share  is  10  times  2  ct.  = 
of  20  t-t.  =  18  ct. 


GENERAL  REVIEW.  107 

10.  In  a  field  containing  55  sheep  and  cows,  \  of  the 
.  =  -J  of  the  sheep:  how  many  are  there  of  each? 

11.  The  sum  of  two  numbers  is  60 ;  and  \  of  the  less 
equals  %  of  the  greater :  what  are  the  numbers  ? 

12.  One-fourth  of  Mary's  age  =  J  of  Sarah's,  and  the 
sum  of  their  ages  is  14  years:  what  is  the  age  of  each? 

13.  Divide  the  number  51  into  two  such  parts,  that  § 
of  the  first  will  equal  f  of  the  second. 

14.  In  an  orchard  of  65  apple  and  peach-trees,  §  of  the 
apple-trees  =  ^  of  the  peach-trees :    how  many  are  there 
of  each? 

15.  From  C  to  D  is  66  mi.;  A  left  C  at  the  same  time 
B   left  D;    when   they  met,   §  of    the    distance   A    had 
traveled  —  -|  of  the  distance  B  had  traveled :   how  much 
farther  did  B  travel  than  A? 

16.  In  an  orchard  of  apple*  plum,  and  cherry-trees,  69 
in    all,   the   plum-trees  =  J  of  the    apple-trees,   and  the 
cherry-trees  =  \  of  the  apple-trees  -f  J  of  the  plum-trees : 
how  many  trees  are  there  of  each  kind? 

17.  The  age  of  Jane  is  -J  of  the  age  of  Sarah,  and  J 
of  both  their  ages  is  f  of  the  age  of  Mary,  which  is  12 
years :  what  are  the  ages  of  Jane  and  Sarah  ? 

18.  How  many  times  ^  of  44  is  twice  that  number  of 
which  i  of  30  is  |? 

19.  John's  money  is  \  of  Charles's ;  and  f  of  John's  -f- 
$33  =  Charles's :  how  much  has  each? 

20.  On  a  farm  there  are  104  animals, — hogs,  sheep,  and 
cows;  there  are  f  as  many  sheep  as  hogs,  and  f  as  many 
cows  as  sheep  :  how  many  are  there  of  each? 

21.  The    time  past  noon  is  equal  to  half  the   time  till 
midnight:  what  o'clock  is  it? 

SOLUTION,     f  +  J=  f ;  f  of  the  time  to  midnight  =  12  hr.:  then, 
\  the  time  to  midnight,  or  the  time  past  noon,  is  \  of  12  hr.  =  4  hr. 


108      RAY'S    NEW   INTELLECTUAL  ARITHMETIC. 

22.  The    time   elapsed    since   noon  is  f  of  the  time  to 
midnight:  what  is  the  hour? 

23.  The  time  past  noon,  -f-  3  hr.,  is    equal  to  \  of  the 
time  to  midnight:  what  is  the  hour? 

24.  What  is  the  hour  in  the  afternoon,  when  the  time 
past  noon  is  equal  to  -J-  of  the  time  past  midnight? 

25.  What  is  the  hour  in  the  afternoon,  when  the  time 
past  noon  is  J  of  the  time  past  midnight? 

26.  What  is  the  hour  of  the  day,  when  \  of  the  time 
past  noon  is  -^  of  the  time  past  midnight? 

LESSON  LVIII. 

1.  What  number  is  that  to  which,  if  its  half  be  added, 
the  sum  will  be  15? 

SOLUTION.     f  +  J  =  f;  f  of   the   number  =  15:    then,  \  of  the 
number  is  ^  of  15  =  5,  and  the  number  is  2  times  5  =  10. 

2.  What   number  is  that   to  which   if  its  §  be  added, 
the  sum  will  be  20? 

3.  If  to  Mary's  age  its  -§•  be  added,  the  sum  will  be  21 
years :  what  is  her  age  ? 

4.  What  number  is  that  which  being  doubled,  and  in 
creased  by  its  -f,  the  sum  will  be  52? 

5.  What    number   is    that   which    being    doubled,    and 
diminished  by  its  %,  the  remainder  will  be  40? 

6.  What    number    is    that    which    being    trebled,    and 
diminished  by  its  |,  the  remainder  will  be  48? 

7.  If  to  David's  age  you  add  its  \  and  its  §,  the  sum 
will  be  26:  what  is  his  age? 

8.  If  to  Sarah's  age  you  add  its  J,  its  J,  and  10  years, 
the  sum  will  be  twice  her  age :  how  old  is  she  ? 

9.  Thomas  spent  •§•  of  his  money,  and  had  30  cents  left : 
how  much  had  he  at  first? 


GENEKAL  KEVIEW.  109 

10.  If  to  a  certain  number  you  add  its  J,  and  its  f  -|-  27, 
the  number  will  be  trebled:  what  is  the  number? 

11.  A  father  is  40  years  older  than  his  son;  the  son's 
age  is  T3T  of  the  father's  age :  what  is  the  age  of  each  ? 

12.  If  to  Susan's  age  you  add  its  -§•  -f- 18  years,  the  sum 
will  be  3  times  her  age :  how  old  is  she  ? 

13.  A  piece  of  flannel,  having  lost  -|  of  its  length  by 
shrinkage,  measured  28  yd. :  what  was  its  length  ? 

14.  The   distance    from  A  to  B  is  J  the  distance  from 
C  to  D,  and  f  of  the  distance  from  A  to  B,  -j-  20  mi.,  = 
the  distance   from  C  to  D :  what  is  the  distance  from  A 
to  B,  and  from  C  to  D? 

15.  My  age  plus  its  J  and  its  £  =  J  of  my  father's  age, 
which  is  69  years:  what  is  my  age? 


LESSON  LIX. 

1.  If  A  can  do  a  piece  of  work  in  2  days,  what  part  of 
it  can  he  do  in  1  day? 

2.  A  can  drink  a  keg  of  cider  in  10  days :  what  part 
of  it  can  he  drink  in  1  day? 

3.  B  can  do  a  piece  of  work  in  J  a  day:    how   many 
times  the  work  can  he  do  in  1  day? 

4.  C  can  mow  a  certain  lot  in  §  of  a  day :  how  many 
such  lots  can  he  mow  in  a  day? 

5.  A  can  mow  a  certain  field  in  2J  days :  what  part  of 
it  can  he  mow  in  1  day? 

6.  B  can  dig  a  trench  in  3^  days :  what  part  of  it  can 
he  dig  in  1  day? 

7.  C  can  walk  from  Cincinnati  to  Dayton  in  3^  days : 
what  part  of  the  distance  can  he  walk  in  2  days  ? 

8.  A  can  do  ^  of  a  piece  of  work  in  1  day,  and  B  J 
of  it :  what  part  of  the  work  can  both  do  in  a  day  ? 


, 


110      RAY'S   NEW   INTELLECTUAL  ARITHMETIC. 

9.  A  can  do  J,  B    J,    and  C  ^  of  a  piece  of  work  in 
1  day:  what  part  of  it  can  they  all  do  in  a  day? 

10.  If  A  can  do  a  piece  of  work  in  2  days,  and  B  in 
3  days :  in  what  time  can  they  both  together  do  it  ? 

SOLUTION. — A  and  B  can  do  J  -f-  £  =  |  of  the  work  in  1  day; 
then,  they  can  do  ^  of  the  work  in  %  of  a  day,  and  the  whole  work  in 
|  —  1£  days. 

11.  A  can  dig  a  trench  in  6  days,  and  B  in  12  days; 
in  what  time  can  they  both  together  do  it? 

12.  C  alone  can  do  a  piece  of  work  in  5  days,  and  B 
in  7  days:  in  what  time  can  both  do  it? 

13.  A  can  do  a  piece  of  work  in  2  days,  B  in  3  days,, 
and  C  in  6  days :  in  what  time  can  all  three  do  it  ? 

14.  A  and  B  mow  a  field  in  4  days ;  B  can  mow  it  alone 
in  12  days:  in  what  time  can  A  mow  it? 

SOLUTION. — A  can  mow  J-  —  iV=  &  of  the  field  in  1  day;  then,  he 
can  mow  the  whole  field  in  6  days. 

15.  A  man  and  his  wife  can  drink  a  keg  of  beer  in  12 
days ;  when  the  man  is  away,  it  lasts  the  woman  30  days ; 
in  what  time  can  the  man  drink  it  alone? 

16.  Three  men,  A,  B,  and  C,  can  together  reap  a  field 
of  wheat  in  4  days ;  A  can  reap  it  alone  in  8  days,  and 
B  in  12  days:  in  what  time  can  C  reap  it? 

17.  A  can  do  a  piece  of  work  in  ^  a  day,  and  B  in  J 
of  a  day:  how  long  will  it  take  both  to  do  it? 

18.  A  can  dig  a  cellar  alone  in  2-J  days,  and  B  in  3J 
days:  in  what  time  can  both  together  dig  it? 

19.  C  can  reap  a   field   of  wheat  in  5  days,  and  D  in 
3J  days:  in  what  time  can  both  reap  it? 


LESSON    LX. 

1.  What  part  of  8  is  2?     What  part  is  4?    Is  1? 

2.  How  many  times   does   10   contain   2?    2   is  what 
part  of  10? 

Ratio   is   the    relation    which    one    quantity   bears   to 
another  of  the  same  kind. 

3.  What  is  the  ratio  of  12  to  2? 

SOLUTION.— The  ratio  of  12  to  2  is  12  -H  2  =  6. 

4.  How  many  times  does  18  contain  9?    What  is  the 
ratio  of  18  to  9  ? 

5.  What  is   the  ratio  of  36  to  12?     45  to  9?     66  to 
11?     52  to  13?     1  to  2?    3  to  4? 

6.  What  is  the  ratio  of  2^  to  5?     6J  to  12J?    J  to  J? 
Off  to  f?    |  to  f?    J  toj? 

7.  If  the  ratio  of  two  numbers  is  5,  and  6  is  the  less 
number,  what  is  the  greater? 

/8.  The  ratio  of  21  to  7  is  equal  to  the  ratio  of  36  to 
some  number:  what  is  the  number? 

9.  Five  less  than  the  ratio  of  20  to  2,  is  J  of  the  ratio 
of  40  to  what  number  ? 

10.  The  ratio  of  18  to   2,  plus  3,  is  7   less  than  the 
ratio  of  38  to  what  number  ? 

11.  The  ratio  of  27  to  9,  increased  by  5,  is  equal  to 
the  ratio  of  20  to  what  number? 

(Ill) 


112      RAY'S   NEW   INTELLECTUAL  ARITHMETIC. 

12.  Divide  25  ct.   between   George  and  John,  so  that 
their  shares  shall  be  in  the  ratio  of  3  to  2. 

SOLUTION. — George's  share  is  3-4-2  =  |  of  John's;  f-|-|  — |;  | 
of  John's  share  are  25  ct.:  then,  John's  share  is  10  ct.,  and  George's 
15  ct. 

13.  Divide  the  number  48  into  two  parts  that  shall  be 
in  the  ratio  of  5  to  7. 

14.  Divide  20  apples  between  A  and  B,  so  that  A  may 
get  2  as  often  as  B  gets  3. 

15.  Divide  28  cents  between  John  and  James,  so  that 
John  may  get  3  as  often  as  James  gets  4. 

16.  In  an  orchard  of  96   trees  there  are  5  apple  trees 
to  3  peach  trees :  how  many  of  each  kind  ? 

17  A  school  of  35  pupils  has  2  boys  to  3  girls:  how 
many  of  each  in  the  school  ? 

18.  What  number  is  that  which  being  added  to  3  times 
itself  will  make  48? 

19.  Mary  has  25  yd.  of  ribbon ;   she  wishes   to  divide 
it  into  two  parts,  so  that  one  shall  be  4  times  the  length 
of  the  other :  what  will  be  the  length  of  each  part  ? 

20.  Divide   28   into   two   parts,  so  that  one  will  be  to 
the  other  as  3  to  4. 

21.  A  and  B  hired   a   pasture   for   $45 :   A  pastured  4 
cows,  and  B  5  cows:  what  should  each  pay? 

22.  Two    men  paid   $3    for  7^  dozen  oysters :  the  first 
paid  $2,  and    the    second,  $1 :    how  many  dozen  oysters 
should  each  have? 

23.  A  and  B  bought  a  horse  for  $40 ;  A  paid  $25,  and 
B  the  rest :    they  sold    him  for   $56 :    what   should   each 
receive  ? 

24.  C  and  D  sold  a  horse   for   $30    less   than  it   cost; 
C's  share  was  to  D's  as  3  to  2:  what  was  each  one's  loss? 


GENEKAL   REVIEW.  113 

LESSON  LXI. 

1.  Divide  the  number  22  into  two  parts  that  shall  be 
to  each  other  as  2J  to  3. 

SOLUTION.— The  first  part  is  2£-=-3  =  f  of  the  second;  £  +  |  = 
JgL;  _y.  of  the  second  part  =  22:  then  the  second  part  is  12  and  the 
first  10. 

2.  Divide    16    apples   between   Henry  and   Oliver,  so 
that  their  shares  shall  be  in  the  ratio  of  1£  to  2^. 

3.  Divide    14   ct.  between  A  and  B,  so   that   B   may 
have  1J  times  as  many  as  A. 

4.  John  and  James  have  together  33  marbles ;  James 
has  If  times  as  many  as  John :  how  many  has  each  ? 

5.  Two  boys  bought  a  silver  watch   for  $7 :    the  first 
paid  $2^,  the  second,  $4J,  and  they  sold  it  for  $28 :  what 
was  each  one's  share? 

6.  William's  age  is  If  times  Frank's  age;  the  sum  of 
their  ages  is  32  yr. :  what  is  the  age  of  each  ? 

7.  A  basket  contains  30  apples :  the  number  of  sound 
ones  is   2J  times  the  number  not  sound :  how  many  are 
there  of  each  ? 

8.  Two  men  built  27  ft.  of  wall :  how  much  did  each 
build,  if  one  built  f  as  much  as  the  other  ? 

9.  Divide  the  number  60  into  3  parts  that  shall  be  to 
each  other  as  3,  4,  and  5. 

SOLUTION,  f  -f-  f  +  f  =\2-;  -1/  of  the  first  part  =  60:  then,  the 
first  part  is  15,  the  second  20,  and  the  third  25. 

10.  Divide  the  number  70  into  four  parts  that  shall  be 
to  each  other  as  1,  2,  3,  and  4. 

11.  Divide    39   into   three   parts  that   shall  be  to  each 
other  as  J,  J,  and  J. 

Int.  8. 


114     RAY'S   NEW   INTELLECTUAL  ARITHMETIC. 

12.  William  had  3  ct.,  Thomas  4  ct.,  and    John  5  ct. ; 
they  bought  36  peaches:  what  was  the  share  of  each? 

13.  A  boat  worth  $864,  of  which  -J   belonged  to  A,  J 
to   B,  and  the   rest   to  C,  was   lost:   what   loss  did  each 
sustain,  it  having  been  insured  for  $500? 

14.  A,  B,  and  C  have  $42  •  B  has  -J  as  much  as  A,  and 
C  -J  as  much  as  B :  how  much  has  each  ? 

15.  Divide  45  ct.  among  A,  B,  and  C,  so   that  A  may 
get  4  ct.  as  often  as  B  gets  3  ct.  and  C  2  ct. 

16.  On  a  farm  there  are  60   animals — horses,  cows,  and 
sheep;    for   each    horse   there    are   3   cows,  and  for  each 
cow  there  are  2  sheep :  how  many  animals  of  each  kind  ? 

17.  Divide  42  plums   among  A,   B,   and   C,  so  that  B 
may  get  twice,  and  C  3  times  as  many  as  A. 

18.  Divide  35  cherries  among  Emma,  Agnes,  and  Sarah, 
so   that  Agnes  shall  have   twice  as  many  as  Emma,  and 
Sarah  twice  as  many  as  Agnes. 


LESSON   LXII. 

1.  If  5  men  can  do  a   piece  of  work   in    18  da.,  how 
many  men  can  do  it  in  9  da.? 

SOLUTION. — In  1  day,  18  times  5  men  =  90  men  can  do  the  work; 
then,  in  9  days,  £  of  90  men  =  10  men  can  do  it. 

2.  If  8   men    can  do  a  piece   of  work  in  15  da.,    how 
many  men  can  do  it  in  12  da.? 

3.  If  8  men  can  do  a  piece  of  work  in  5  da.,  in  what 
time  can  5  men  do  it.? 

4.  If  9  pipes  fill  a  cistern  in  2J  hr.,  in  what  time  will 
5  such  pipes  fill  it? 

5.  A  man,  failing  in  business,  paid  80  ct.  on  each  dol- 


GENEKAL  REVIEW.  115 

lar  of  his  indebtedness :    what  did  I  receive,  if  ho  owed 
ine  $60? 

SOLUTION.— 80  cts.  =  $f .     I  received  GO  times  $f  =  $48. 

6.  A  grocer,  failing,  pays    only  15    ct.    on  the  dollar: 
what  will  a  creditor  receive  to  whom  he  owes  $80? 

7.  A  trader,  failing,  pays    60  ct.  on  the*  dollar:    what 
will  a  creditor  receive  to  whom  he  owes  $80? 

8.  If    a   certain    quantity   of  flour    afford    8   five-cent 
loaves,  how  many  ten-cent  loaves  will  it  furnish? 

SOLUTION. — It  will    afford  5  times  8,  or  40,  one-cent  loaves;  and 
•^  of  40,  or  4,  ten-cent  loaves. 

9.  If  a    certain   quantity    of    flour    afford    6    five-cent 
loaves,  how  many  three-cent  loaves  will  it  furnish? 

10.  If  a  sack  of  flour  make  20  three-cent  loaves,  how 
many  four-cent    loaves   will   it  make?     How  many  five- 
cent  loaves? 

11.  If  a   loaf  weigh  8  oz.  when  flour  is  $3    a   barrel, 
what  should  it  weigh  when  flour  is  $4  a  bbl.  ?     $5  a  bbl.  ? 

12.  A  loaf  weighs  10  oz.  when  flour  is  $6  a  bbl. :  what 
should  it  weigh  when  flour  is  $5  a  bbl.  ? 

13.  If  a    loaf  weigh    7    oz.  when    flour  is   $5J-  a  bbl. : 
what  ought  it  to  weigh  when  flour  is  $4f  a  bbl.? 

14.  If  5  men  can  do  a  piece  of  work  in  a  certain  time, 
how    many   can    do  a  piece   twice    as   large    in  -J-  of  the 
time? 

15.  If  6  men  can  do  a   piece  of  work    in    5    days,  in 
what  time  can  they  do  it,  if  they  receive  the  assistance 
of  3  additional  men  when  the  work  is  half  completed? 

16.  If  7  men    can    do   a   piece  of  work  in  4  days,  in 
what  time  can  it  be  done,  if  3  of  the   men    leave  when 
the  work  is  half  completed? 


116      RAY'S    NEW   INTELLECTUAL   ARITHMETIC. 

17.  If  the    wages   of  3  men  for  5    days   is    $30,  what 
will  be  the  wages  of  4  men  for  7  da.  ? 

SOLUTION.— The  wages  of  1  man  for  5  days  is  £  of  $30  —  $10,  and 
the  wages  of  1  man  for  1  day  is  £  of  $10  =  $2;  then,  the  wages  of  1 
man  for  7  days  is  7  times  $2  =  $14,  and  the  wages  of  4  men  for  7  days 
is  4  times  $14  =$56. 

* 

18.  If  6   persons   spend  $36   in  8  days,  how  much,  at 
that  rate,  would  5  persons  spend  in  12  da.? 

19.  If  3  men  can  build    12    rd.  of  wall  in  8  da.,  how 
many  rd.  can  5  men  build  in  3  da.  ? 

20.  If  6    horses    eat   36    bu.  of  oats  in  10    days,  how 
many  bu.  will  5  horses  eat  in  9  da.  ? 

21.  If  5    oxen    eat    2    A.  of  grass   in    6  days,  in  how 
many  days   will    12    oxen    eat    8    A.,  the   grass  growing 
uniformly  ? 

22.  If  a   family  of  8    persons    spend  $400  in  5  mon., 
how  much  would  maintain  them  8  mon.,  if  3  more  per- 
sons were  added? 

23.  If  10   oxen  can  be  kept  on  5  A.  for  3  mon.,  how 
many  sheep  can  be  kept  on  15  A.  for  5  mon.,  if  7  sheep 
eat  as  much  as  1  ox? 


LESSON  LXIII. 

1.  A  and  B  rent    a    pasture    for    $25 :    A    puts    in    27 
oxen,  and  B  180  sheep :  what  should  each  pay,  supposing 
an  ox  to  eat  as  much  as  10  sheep? 

SOLUTION.— 180  sheep  eat  as  much  as  180 -=-10  =18  oxen.  B 
should  pay  18-=-27^f  as  much  as  A;  then,  f  -f  §  =  f:  f  of  what 
A  should  pay  are  $25:  then,  A  should  pay  $15,  and  B  $10. 

2.  A    and  B  rent   a    pasture    for   $60 :    A    puts    in  14 


GENEKAL  KEVIEW.  117 

horses,    and   B,   15    cows :    what   should   each   pay,  if  2 
horses  eat  as  much  as  3  cows? 

3.  A    and    B   rent    a    pasture   for    $72 :    A  puts    in    8 
horses,  B  15  oxen  and  120  sheep :  what  should  each  pay, 
if  a   horse    eat    as   much   as    20    sheep,  and  2  horses  as 
much  as  3  oxen? 

4.  A    and   B    rent    a   pasture    for   $35 :    A   puts   in   4 
horses    2    wk. ;    B,  3  horses  4  wk. :    what   ought  each  to 
pay? 

SOLUTION. — 4  horses  in  2  wk.  eat  the  same  as  1  horse  in  4  times 
2  =  8  wk.;  and  3  horses  in  4  wk.  eat  the  same  as  1  horse  in  3  times 
4=12  wk.;  then,  B  ought  to  pay  12-r-8  =  f  as  much  as  A,  or  $3 
when  A  pays  $2;  whence,  A  pays  $14,  and  B  $21. 

5.  C  and  D  join  their  stocks  in  trade ;    C  puts  in  $50 
for  4  mon.,  and  D  $60  for  5  mon. :  they  gain  $45 :  what 
is  the  share  of  each  ? 

6.  Two   masons,  A    and   B,  built   a   wall  for   $81;    A 
sent   3    men   for    4   da.,  and   B  5  men   for  3  da. :   what 
ought  each  to  receive? 

7.  A  and  B  traded  in  company;    A  put  in  $2  as  often 
as  B  put  in  $3;    A's  money  was  employed    5  mon.,  and 
B's    4   mon. :    they   gained    $55 :    what   was    each   man's 
share  ? 

8.  E  and  F  rented  a  field  for  $27 ;    E  put  in  4  horses 
for  5  mon.,  and  F  10  cows  for  6  mon. :  what  ought  each 
to  pay,  if  2  horses  eat  as  much  as  3  cows? 

9.  M  and  N  enter  into  partnership    for  one   year.     M 
puts  in  $600,  and  N,  $900 ;  they  gain  $300 :  after  paying 
$150  expenses,  what  is  each  one's  share  of  the  gain? 

10.  At  the  beginning  of  the  year,  C  went  into  business 
with  a  capital  of  $600 :    four   months   after,  D  formed  a 
partnership   with    C,  and   put   in  $600 :  the  gain  for  the 
year  was  $250:  what  was  each  one's  share? 


118      RAY'S    NEW    INTELLECTUAL   ARITHMETIC. 

11.  E  and  F  entered  into  partnership  for  a  year;   E's 
capital  was  $1000,  and  F's   three  times  as  much  ;  at  the 
end  of  8  months,  F  drew  out  $1000;  the  gain  for  the  year 
was  $770 :  what  was  each  one's  share  ? 

12.  The   capital  of  a  firm,  consisting  of  A  and  B,  was 
$2400 ;  the  gain   for   the  year  was  $240,  A's  share  being 
$20  more  than  B's :  how  much  capital  did  each  furnish  ? 

13  The  capital  of  a  firm,  consisting  of  C  and  D,  was 
$980;  C's  capital  was  used  8  months,  and  D's  6  months, 
when  the  gain  was  equally  divided:  how  much  capital 
did  each  invest? 

14.  In  a  partnership,  A's   gain  was    $70,  and  B's  $80 
A's  capital  was  employed  10  months,  and  B's  8  months: 
their  joint   capital   was    $1700 :    what   was   the   original 
investment  of  each  ? 

15.  The  gain  of  a   firm,  consisting  of  E   and  F,  was 
$840 :  E's  stock  was  to  F's  as  2  to  3,  and  E's  was  in  use 
10  months,  F's  12  months :  what  was  each  one's  share  of 
the  gain? 


LESSON    LXIV. 

Any  per  cent  of  a  number  is  so  many  hundredths  of  it  ; 
thus,  one  per  cent  of  a  number  is  yj^  of  it. 


1.  What  part  is    2  per  cent? 
SOLUTION.  —  2  per  cent  is  Tfo  =  -fa. 

2.  What  part  is     4  per  cent?  5?  6?     8? 

3.  What  part  is  10  per  cent?  12?  15? 

4.  What  part  is  16  per  cent?  20?  24? 

5.  What  part  is  25  per  cent?  28?  30? 

6.  What  part  is  32  per  cent?  35?  36? 

7.  What  part  is  40  per  cent?  45?  48? 

8.  What  part  is  50  per  cent?  60?  70? 

9.  What  part  is  75  per  cent?  80?  90? 

10.  What  part  is  2J  per  cent? 

SOLUTION.    2J  =  jj.     1  per  cent  is  T^;  then,  £  per  cent  is  \  of 
—  »iff»  and  I  Per  cent  is  5  times  liff  =¥ff- 

11.  What  part  is     3£  per  cent?  6J? 

12.  What  part  is     6f  per  cent?  7J? 

13.  What  part  is     8J  per  cent?  12J? 

14.  What  part  is  13J  per  cent?  16§? 

15.  What  part  is  17^  per  cent?  18|? 

16.  What  part  is  23J  per  cent?  31  J? 

(119) 


120       RAY'S  NfiW  INTELLECTUAL  ARITHMETIC. 

17.  What  part  is  37£  per  cent?     43f  ? 

18.  What  part  is  56J-  per  cent?     624? 

19.  What  part  is  66f  per  cent? 

20.  What  part  is  87 J  per  cent? 

LESSON  LXV. 

1.  What  is    4    per  cent  of  50? 
SOLUTION. — 4  per  cent  is  -fa:     fa  of  50  =  2. 

2.  What  is     6     per  cent  of  50?     100? 

3.  What  is  10    per  cent  of  20?       30? 

4.  What  is  12£  per  cent  of  24?      48? 

5.  What  is  25     per  cent  of  $32?     $80? 

6.  What  is  33J  per  cent  of  51  bushels  ? 

7.  What  is  50     per  cent  of  14  horses? 

8.  I   bought   a  piece  of  cloth    for  $32,  and  sold  it  so 
as  to  gain  6 J  per  cent :  what  did  I  gain  ? 

SOLUTION. — 6£  per  cent  is  fa:     I  gained  fa  of  $32  =  $2. 

9.  A  grocer  bought  a  bbl.   of  sugar  for  $10,  and  in 
selling  it  gained  10  per  cent :  how  much  did  he  gain  ? 

10.  A  farmer,  having  a  flock   of  40  sheep,  lost  5  per 
cent  of  them:  how  many  had  he  left? 

11.  A  flock  of  50   sheep   increases  10  per  cent  in  one 
year:  how  many  are  then  in  the  flock? 

12.  A  lady,  having  $20,  spent   10  per  cent  for  muslin, 
and  10  per  cent  of  the  remainder  for  calico :    how  much 
did  she  pay  for  both  ? 

13.  I  paid  30   ct.   per  yd.  for  cambi-ic:    at  what  price 
must  I  sell  it,  to  make  10  per  cent? 

SOLUTION. — 10  per  cent  is  fa.     I  must  gain  fa  of  30  ct.  =  3  ct.; 
then  I  must  sell  it  for  30  ct.  +  3  ct.  =  33  ct. 


PERCENTAGE.  121 

14.  To  make  12 J  per  cent  profit,  what  must  muslin  be 
sold  at  that  cost  8  ct.  per  yd.?     16  ct.  ? 

15.  To  make  8J-  per  cent  profit,  what  must  sugar  bo 
sold  for  that  cost  6  ct.  per  Ib.  ?     18  ct.  ? 

16.  To  make  25  per  cent  profit,  what  must  delaine  be 
sold  for  that  cost  12  ct.  per  yd.  ?     16  ct.  ?     20  ct.  ?     35  ct.  ? 


LESSON   LXVI. 

1.  How  many  per  cent  is     J? 
SOLUTION. — It  is  £  of  100  =  50  per  cent 

2.  How  many  per  cent  is     J?       §?       J? 

3.  How  many  per  cent  is     J?       ^?       J? 

4.  How  many  per  cent  is     f  ?       f?       -J-? 

5.  How  many  per  cent  is     -J?       -|?       -|? 
G.  How  many  per  cent  is  T^?    T%?     y7^? 

7.  How  many  per  cent  is  y^?     y^-?     T5^? 

8.  How  many  per  cent  is  y1-?    y1^-?    y3^? 

9.  How  many  per  cent  is 

10.  How  many  per  cent  is 

11.  How  many  per  cent  is  ^? 

12.  How  many  per  cent  is 

13.  How  many  per  cent  is 

14.  How  many  per  cent  is 

15.  How  many  per  cent  is 

16.  How  many  per  cent  is 

17.  How  many  per  cent  is 

18.  How  many  per  cent  is  -^f  ?     -^f  ? 

19.  How  many  per  cent  is  ^|?     J|? 

20.  How  many  per  cent  is  -^?    ^f  ? 

21.  How  many  per  cent  is  -|f  ?     ||? 

22.  How  many  per  cent  is  J|? 


122      KAY'S    NEW   INTELLECTUAL  ARITHMETIC. 


LESSON    LXVII. 

1.  Two  is  what  per  cent  of  5? 
SOLUTION.  —  2  is  f  of  5:     f  =  TY<j,  or  40  per  cent. 

2.  Three  is  what  per  cent  of  5?     Of  12? 

3.  Four  is  what  per  cent  of  8?     Of  32? 

4.  Five  dollars  are  what  per  cent  of  $20  ?    $30  ? 

5.  Eight  men  are  what  per  cent  of  160  men? 

6.  There  are  36  pupils  enrolled  in  a  certain   school;  if 
9  are  absent,  what  is  the  per  cent  of  absence  ? 

7.  Out  of  60  pupils  in  a  school,  20  study  geography: 
what  per  cent  is  that  of  the  whole  number  ? 

8.  There  are   45  pupils   enrolled  in  a  certain  primary 
school  ;  on   a  certain   day  only  30  of  them  were  present, 
what  was  the  per  cent  of  attendance  ? 

9.  A  grocer  buys  coifee  at   25  ct.  per  pound,  and  sells 
it  at  a  profit  of  5  ct.  per  pound  :  what  is  his  gain  per 
cent? 

10.  A  merchant  bought  cloth  at  $5   per  yard,  and  sold 
it  at  $7  per  yard  :  what  per  cent  did  he  gain  ? 

SOLUTION.—  Ho  gained  $7  —  $5  =  $2:     $2  arc  f  of  the  cost;  f  are 
40  per  cent. 

11.  James  bought  a  melon  for  4  ct.,  and  sold  it  for  5 
ct.  :  what  per  cent  did  he  gain? 

12.  An  orange  was  bought  for  5  ct.,  and  sold  for  4  ct.  : 
what  was  the  per  cent  of  loss? 

13.  Thomas  bought  a  watch  for  $4,  and  sold  it  for  $6  : 
what  per  cent  did  he  gain? 

14.  Henry  bought  a  horse  for  $15,  and  sold  it  for  $24: 
what  per  cent  did  he  gain? 


PEKCENTAGE.  123 

1.5.  A  keg  of  wine  holding  5  gal.,  lost  6  qt.  by  leakage : 
what  was  the  loss  per  cent  ? 

16.  By  selling  citrons  at  6  ct.  each,  John   cleared  £  of 
the  first  cost:  what  per  cent  would  he   have  cleared  by 
selling  them  at  8  ct.  each? 

17.  A  merchant  bought  cloth  at  the  rate  of  6  yd.  for  $3., 
and  sold  it  at  the  rate  of  5  yd.  for  $4 :  what  per  cent  did 
he  gain? 

18.  Henry  sold  melons  at  8  ct.  each,  and  lost  ^  of  the 
first  cost :    what  per  cent  would  he  have  lost   by  selling 
them  at  3  for  25  ct. :  what  per  cent  would  he  have  gained 
by  selling  them  at  2  for  25  ct.  ? 

19.  James  bought  a  lot  of  lemons,  at  the  rate  of  2  for 
3  ct. ;  but,  finding  them  damaged,  he  sold  them  at  the  rate 
of  3  for  2  ct. :  what  per  cent,  did  he  lose  ? 


LESSON    LXVIII. 

1.  Sold  a  watch  for  $12,  and  gained  20  per  cent:  what 
was  the  cost? 

SOLUTION. — 20  per  cent  is  ^;  f-f-£  =  f;  |  of  the  cost  are  $12, 
then,  the  cost  is  $10. 

2.  I  sold  a  piece  of  cloth  for  $26,  and  gained  30  per 
cent:  what  did  the  cloth  cost  me? 

3.  If  there    is    a   gain  of  40  per  cent  when  muslin  is 
sold  at  14  ct.  a  yd.,  what  is  the  cost  price? 

4.  By  selling  a  horse  for   $81,  there  was  a  gain  of  12  J 
per  cent :  what  did  the  horse  cost  ? 

5.  Sold  a  horse   for   $63,  and   lost  10  per  cent:    what 
was  the  cost? 

6.  Thomas   sold  a  watch   for  $21,  and   gained    75    per 
cent:  what  did  he  pay  for  it? 


124      KAY'S    NEW   INTELLECTUAL   AK1TIIMETIC. 

7.  James   sold  10  oranges    for  40   ct.,  and   gained    33J 
per  cent:  bow  much  did  each  orange  cost? 

8.  Sold  a  watch    for  $10,  by  which    I   gained    25    per 
cent:    what  would  I  have  gained   by  selling   it  for  $12? 

9.  By  selling   muslin  at   7    ct.  per  yd.,  there  is  a  loss 
of  12  J  per  cent:  what  will  be  the  loss  per  cent  by  sell- 
ing it  at  6  ct.  per  yd.? 

10.  By  selling   my  horse   for  $35,  there  was  a  loss   of 
16f  per  cent:    what  would  have  been  the  gain  per  cent 
by  selling  him  for  $63? 

11.  I  bought  a  watch  for  $18,   which  was  20  per  cent 
more  than  its  value:    I  sold  it  at  10  per  cent  less  than 
its  value:  what  sum  did  I  lose? 

12.  A  sold  B  a  watch  for  $60,  and  gained  20  per  cent: 
afterward  B  sold  it  and  lost  20  per  cent  on  what  it  cost 
him:  how  much  did  B  lose  more  than  A  gained? 

13.  A  watch-maker  sold  two  watches  for  $30  each :  on 
one  he  gained  25  per  cent,  and  on  the  other  he  lost  25 
per  cent:  how  much  did  he  lose  by  the  sale? 

14.  By  selling  4  apples  for  3  ct.,  a  dealer  gains  50  per 
cent:  what  per  cent  will  he  gain  by  selling  them  at  the 
rate  of  5  for  4  ct,  ? 

15.  Sold  5  lemons  for  4  ct,  and  lost  20  per  cent:  what 
per  cent  did  I  lose  by  selling  6  for  5  ct.  ? 

16.  Two-thirds  of  10  per  cent  of  60  are  J  of  what  per 
cent  of  40? 

17.  One-half  of  f  of  50  per  cent  of   120  is  10  less  than 
20  per  cent  of  what? 

18.  One-fourth  of  §  of  60  per  cent  of  10  is  5  less  than 
50  per  cent  of  what? 

19.  Three-fourths  of  f  of  75  per  cent  of  15  are  If  more 
than  50  per  cent  of  what? 

20.  One  and  one-half  times  §  of  25  per  cent  of  4  are  25 
per  cent  of  J  of  what  number? 


PERCENTAGE.  125 

LESSON  LXIX. 

Allowances  made  to  purchasers  by  wholesale  dealers 
are  called  per  cents  off. 

10  per  cent  off  means  10  per  cent,  or  y1^,  from  the 
retail,  or  list  price. 

£  off  means  £,  or  12-J  per  cent,  from  the  list  price. 

20/5  (read  20  and  5)  means  20  per  cent  off,  and  5  per 
cent  taken  from  the  remainder. 

J-  and  5  means  12^  per  cent  off,  and  5  per  cent  taken 
from  the  remainder. 

1.  The   price   of  a   book   was  $3,  but  the  book-seller 
allowed  20  per  cent  off:  what  was  paid  for  the  book? 

2.  The   amount  of  a  bill  of  goods  was   $125,  but   the 
dealer  allowed  ^  off:  what  was  paid  for  the  goods? 

3.  A  bill  of  goods   amounted  to  $840,  and    the  dealer 
gave  ^  off:  what  was  paid  for  the  goods? 

4.  A   lot   of  books  amounted  to  $500 :   the  book-seller 
allowed  20/5  off:  what  was  paid  for  the  books? 

5.  A  bill  of  goods  amounted  to  $1200,  and  the  dealer 
allowed  -J  and  5  off:  what  was  paid  for  the  goods? 

6.  Paid  $4.80  for  a  book,  the  book-seller  having  allowed 
me  20  per  cent  off:  what  was  the  retail  price? 

7.  Paid   $720    for   a  bill   of  goods,  the    dealer   having 
allowed  J  off:  what  was  the  retail  price? 

8.  Paid  $133  for  goods,  the  dealer  having  allowed  20/5 : 
what  was  the  list  price? 

9.  Paid   $399    for   goods,  the   dealer  having  allowed  j- 
and    5   per  cent   for   cash,  and  sold  them  at    the  list  or 
retail  price:  what  did  I  get  for  the  goods. 

10.  The   retail   price  of  a  bill   of  goods  was  $70 ;    the 
dealer  allowed  20/5  on  $50,  and  10/5  on  the  remainder 
of  the  amount:  what  was  paid  for  the  goods? 


126       KAY'S  NEW  INTELLECTUAL  ARITHMETIC. 

LESSON   LXX. 

Commission   is   the   sum   allowed  to  agents  for  buying, 
selling,  or  transacting  other  business. 

1.  An    agent   sold  a  house  for  $4000,  charging  2^  per 
cent  commission :  what  was  his  commission  ? 

2.  An   agent    sells    goods  to  the  amount  of  $560,  at  5 
per  cent  commission:  Avhat  is  the  commission? 

3.  A  commission    merchant   sells  1000  bu.  of  corn,  for 
50  ct.  a  bu.,  and  charges  2^   per   cent  for  selling:  what 
is  his  commission? 

4.  An  agent  sells  5  village  lots,  for  $300  each,  charging 
5  per  cent:  what  is  his  commission,  and  how  much  does 
the  owner  receive? 

5.  A  farmer  sends  800  bu.  of  wheat   to   a  commission 
merchant,  who  sells  it  at  $1.25  a  bu.,  and  charges  2  per 
cent  commission :  how  much  does  the  farmer  receive  for 
his  wheat? 

6.  A  collector  received    $100   for   collecting   bills,  at  5 
per  cent  commission:  how  much  did  ho  collect? 

7.  A  merchant  allowed  a  collector  10  per  cent  for  col- 
lecting bills :    the    commission    was  $60 :    how  much  was 
collected  ? 

8.  A  commission  merchant  sold  grain  for  $1000,  charg- 
ing 5  per  cent,  and    invested   the   remainder   in    shares, 
at  $50  a  share,  without  extra  charge:  how  many  shares 
did  he  buy? 

LESSON    LXXI. 

A  Policy  is  the  written  agreement  of  an  Insurance 
Company  to  pay  a  certain  sum  of  money  in  case  of  loss 
by  fire,  water,  accident,  or  other  hazard. 


PEKCENTAGE.  127 

Tho  Premium  is  the  sum  paid  for  insurance. 

1.  What  is  paid  for  an  insurance  policy  of  $2000,  at  J 
per  cent  premium? 

2.  A  house   worth  $3000  is   insured  for  £  its  value,  at 
2  per  cent  premium:  what  is  the  insurance? 

3.  What    does  it  cost  to  insure  property  worth  $2400, 
for  f  its  value,  at  1  per  cent,  the  policy  costing  $1.50? 

4.  A  man  insured  his  house  for  $2500,  and  his  furni- 
ture for  $1500,  at   a   premium  of  f  per  cent:    what  did 
he  pay? 

5.  A  man's  house  was  worth  $1800,  and  his  furniture, 
$1200:    he   insured  both  at   §   their  value,  paying  1  per 
cent  premium  on  the  house,  \  per  cent  premium  on  the 
furniture,  and  $1  for  the  policy:  how  much  did  he  pay? 

6.  A  man's  house  was  worth  $2600,  and  his  furniture, 
$1500 :  he  insured  the  house  at  \  its  value,  and  the  fur- 
niture at  f :    he  paid  2  per  cent  premium  on  the  house, 
1  per   cent   on    the   furniture,  and  $1.50  for  the   policy: 
how  much  did  he  pay? 

LESSON   LXXII. 

Interest  is  money  paid  for  the  use  of  money. 
The  Principal  is  the  sum  of  money  which  is  loaned. 
The  Amount   is   the   principal    and    interest    added  to- 
gether. 

1.  What  is  the  interest  of  $2  for  3  yr.,  at  5  per  cent? 

SOLUTION. — The  interest   for   3  yr.  is    3  times   5  =  15  per  cent; 
15  per  cent  is  2%;  ^  of  $2  =  30  ct. 

2.  Find  the  interest  of    $5  for  2  yr.,  at  6  per  cent. 

3.  Find  the  interest  of    $8  for  5  yr.,  at  5  per  cent. 

4.  Find  the  interest  of  $20  for  3  yr.,  at  8  per  cent. 

5.  Find  the  interest  of  $25  for  6  yr.,  at  4  per  cent. 


128  KAY'S  NEW  INTELLECTUAL  ARITHMETIC. 

6.  Find  the  interest  of  $40  for  4  yr.,  at  5  per  cent. 

7.  Find  the  interest  of  $50  for  3  yr.,  at  6  per  cent. 

8.  Find  the  interest  of  $60  for  2  yr.,  at  7  per  cent. 

9.  Find  the  interest  of  $75  for  3  yr.,  at  4  per  cent. 
10.  Find  the  interest  of  $80  for  5  yr.,  at  9  per  cent. 


LESSON  LXXIII. 

1.  What  the  interest  of  $50  for  6  mo.,  at  6  per  cent? 

SOLUTION. — 6  mo.  are  £  yr.;  the  interest  for  £  yr.  is  £  of  6  per 
cent  =  3  per  cent;  3  per  cent  is  T§^;  jf^  of  $50  =  $1  and  50  ct. 

2.  Find  the  interest  of  $60  for  4  mo.,  at  5  per  cent. 

3.  Find  the  interest  of  $80  for  7  mo.,  at  6  per  cent. 

4.  Find  the  interest  of  $40  for  9  mo.,  at  8  per  cent. 

5.  Find  the  interest  of  $75  for  8  mo.,  at  9  per  cent. 

What  is  the  interest 
G.  Of  $120  for    6  mo.  15  da.,  at  6  per  cent? 

SOLUTION. — 6  mo  15  da.  are  ||  yr  ;  the  interest  for  ||  yr.  is  ||  of 
6  per  cent  —  a?3-  per  cent;  *£  per  cent  is  ^&;  ^  of  $120  =  $3.90. 

7.  Of  $180  for  10  mo.  10  da.,  at  4  per  cent? 

8.  Of    $45  for  11  mo.  23  da.,  at  8  per  cent? 

SOLUTION. — The  interest  of  $45  for  1  year  is  $3.60;  for  1  month, 
^  of  $3.60  =  30  ct.;  and  for  1  day,  ^  of  30  ct.  —  1  ct.  The  interest 
for  11  months  is,  therefore,  $3.30;  for  23  days,  23  ct.;  and  the  total 
interest  is  $3.53. 

9.  Of  $200  for    4  mo.  24  da.,  at  6  per  cent? 

10.  Of  $480  for  9  mo.  18  da.,  at  5  per  cent? 

11.  Of  $360  for  5  mo.  19  da.,  at  5  per  cent? 

12.  Of  $144  for  8  mo.  25  da.,  at  4  per  cent? 

13.  Of    $40  for  1  yr.   4   mo.,  at  6  per  cent? 


PERCENTAGE.  129 


14.  Of    $60  for    2  yr.    3    mo.,  at  5  per  cent? 

15.  Of    $75  for    1  yr.   3   mo.    6  da.,  at  4  per  cent? 

What  is  the  amount 

16.  Of  $25  for  3  yr.,  at  4  per  cent? 

17.  Of  $40  for  2  yr.,  at  5  per  cent? 

18.  Of  $55  for  3  yr.,  at  8  per  cent? 

19.  Of  $30  for  1  yr.,  4  mo.,  at  7  per  cent? 

,20.  Of  $50  for  2  yr.    3  mo.    6  da.,  at  6  per  cent? 
21.  Of  $90  for  1  yr.    3  mo.    6  da.,  at  8  per  cent? 


LESSON  LXXIV. 

1.  The    interest   of  a  certain    principal  for  2  yr.,  at  6 
per  cent,  is  $3 :  what  is  the  principal  ? 

SOLUTION. — The  interest  is  12  per  cent  =  fa]  then,  fa  of  the  prin- 
cipal are  $3;  whence  the  principal  is  $25. 

2.  The    interest    of  a    certain  principal  for  3  yr.,  at  4 
per  cent,  is  $6:  what  is  the  principal? 

3.  What  principal  at  interest  for  4  yr.,  at  5  per  cent, 
will  produce  $12  interest? 

4.  What  principal  at  interest  for   5   yr.,  at  8  per  cent, 
will  produce  $30  interest? 

5.  What  principal  at  interest  for  4  yr.,  at  7^  per  cent, 
will  produce  $42  interest? 

6.  What   principal    at   interest    for  2  yr.    6   mo.,   at    6 
per  cent,  will  produce  $36  interest? 

7.  What    principal    at    interest   for   3  yr.  4   mo.,  at    6 
per  cent,  will  produce  $70  interest? 

8.  A  father   wishes    to   place    such  a  sum    at   interest, 
at  5  per  cent.,  -as   will   produce    for   his    son   an   annual 
income  of  $200:  what  sum  must  he  invest? 

Int.  9. 


130      BAY'S    NEW   INTELLECTUAL   ARITHMETIC. 

LESSON  LXXV. 

1.  What  principal  on  interest  for  2  yr.,  at  5  per  cent, 
will  amount  to  $55? 

SOLUTION. — The  interest  is  10  per  cent  =  j1^;  then,  ^  -\-  ^  =  ££; 
^  of  the  principal  are  $55;  whence  the  principal  is  $50. 

What  principal  on  interest, 

2.  At     6  per  cent,  for  3  yr.,  will  amount  to  $236? 

3.  At     5  per  cent,  for  4  yr.,  will  amount  to  $600? 

4.  At  10  per  cent,  for  5  yr.,  will  amount  to  $375? 

5.  At     6  per  cent,  for  5  yr.,  will  amount  to  $390? 

6.  The  amount   due   on  a  note  which  has  been  on  in- 
terest  3   yr.  4    mo.,  at   6  per  cent,  is  $30 :   what  is  the 
face  of  the  note? 

7.  The  amount  of  two-fifths  of  A's  money  on   interest 
for  2  yr.  6  mo.,  at  8  per  cent,  is  $60 :  what  is  his  whole 
principal  ? 

LESSON  LXXVI. 

1.  In  what   time,  at    6  per  cent,  will  $50  give  $10  in- 
terest? 

SOLUTION. — The  interest  for  1  yr.  is  $3;  then,  the  time  will  be  as 
many  years  as  $3  are  contained  times  in  $10,  which  arc  3 J  =  3  yr. 
4  mo. 

In  what  time, 

2.  At     5  per  cent,  will     $40  give     $8  interest? 

3.  At     8  per  cent,  will     $75  give  $15  interest? 

4.  At  10  per  cent,  will     $60  give  $16  interest? 

5.  At     5  per  cent,  will  $140  give  $24  interest? 

6.  At     6  per  cent,  will     $25  give  $10  interest? 


PERCENTAGE.  131 

7.  In    what   time,  at  4  per  cent,  will   any  given  prin- 
cipal double  itself? 

SOLUTION. — Any  principal  will  double  itself  in  as  many  years  as  4 
per  cent  is  contained  times  in  100  per  cent,  which  are  25. 

8.  In  what  time  will  any  given  principal   double  itself, 
at  2  per  cent?     At  3  per  cent?     At  5  per  cent?     At  6 
per  cent?     At  7  per  cent?     At  8?     At  10?     At  12? 

9.  In  what  time  will  any  given  principal  treble  itself, 
at  5  per  cent? 

10.  In  what  time  will  any  given  principal  treble  itself, 
at  8  per  cent?     At  10  per  cent? 


LESSON  LXXVII. 

1.  At  what   per  cent  will  $200,  in  2  yr.,  give  $24  in- 
terest ? 

SOLUTION.— The  interest  for  1  yr.  is  f  of  $24  =  $12;  this  is  ^  =» 
^  of  the  principal;  33^  are  6  per  cent. 

At  what  per  cent, 

2.  Will     $50  in  5  yr.,  give  $20     interest? 

3.  Will     $75  in  3  yr.,  give  $11J  interest? 

4.  Will  $300  in  3  yr.,  give  $63     interest? 

5.  Will  $300  in  2  yr.    3  mo.,  give  $54  interest? 

6.  Will  $240  in  3  yr.    4  mo.,  give  $56  interest? 

7.  Will  $200  in  4  yr.,  amount  to  $240? 

8.  Will  $150  in  3  yr.    8  mo.,  amount  to  $183? 

9.  Will  any  given  principal  double  itself  in  20  yr.  ? 

SOLUTION. — Any  principal  will  double  itself  at  -£§  of  100  =  5  per 
cent. 

10.  At  what   per  cent  will  any  given  principal  double 
itself  in  12  yr.  ?    In  10  yr.  ?    8  yr.  ?    5  yr.  ?    4  yr.  ?    2  yr.  ? 


132      RAY'S    NEW   INTELLECTUAL  ARITHMETIC. 

LESSON  LXXVIII. 

discount  corresponds  to  interest,  but  is  paid  in  advance1, 
present  worth  corresponds  to  principal ;  and  the  sum  given, 
to  amount. 

1.  What   is    the   present  worth  and  discount,  at  5  per 
cent,  of  a  note  for  $72,  due  4  yr.  hence  ? 

SOLUTION.— The  discount  is  20  per  cent  —  £;  $-f-|  =  •§;  then,  f 
of  the  present  worth  =  $72;  whence  the  present  worth  is  $60,  and 
the  discount  $12. 

2.  What  is  the   present  worth  and  discount,  at    6    per 
cent,  of  a  note  for  $520,  due  5  yr.  hence  ? 

3.  What  is  the   present  worth  and  discount,  at   4   per 
cent,  of  a  note  for  $30,  due  5  yr.  hence? 

4.  What  is  the  present  worth  and    discount,  at  10  per 
cent,  of  a  note  for  $750,  due  5  yr.  hence  ? 

5.  What  is  the  discount,  at  5  per  cent,  of  a   note   for 
$345,  due  3  yr.  hence? 

6.  What  is  the  discount,  at    6   per  cent,  of  a  note  for 
$496,  due  4  yr.  hence? 

7.  What  is  the  discount,  at   5   per  cent,  of  a  note  for 
$24,  due  4  yr.  hence? 

8.  What  is  the  present  worth,  at  6  per  cent,  of  a  note 
for  $65,  due  5  yr.  hence? 

9.  What  is  the  present  worth,  at  5  per  cent,  of  a  note 
for  $55,  due  5  yr.  hence? 

10.  What  is    the   present   worth,  at    6    per   cent,  of  a 
note  for  $77,  due  6  yr.  8  mo.  hence? 

11.  What  is  the  discount,  at   7   per   cent,  of  a  note  for 
$1000,  due  in  3  yr.  6  mo.? 

12.  What  is  the  discount,  at   8   per   cent,  of  a  note  for 
$900,  due  in  2  yr.  9  mo.? 


PERCENTAGE.  133 

LESSON  LXXIX. 

1.  At  6  per  cent,  for   4   yr.  2  mo.,  what   part   of  tho 
principal  is  equal  to  the  interest? 

2.  At  5  per  cent,  for  5  yr.,  what  part  of  the    amount 
is  equal  to  the  interest? 

3.  When  the   interest   for    2   yr.  =  -i  of  the   principal, 
what  is  the  rate  per  cent? 

4.  When  the  interest  for  2  yr.  6  mo.  =  J  of  the  prin- 
cipal, what  is  the  rate  per  cent? 

5.  When  the  interest,  at  10  per  cent.  =  ^  of  the  prin- 
cipal, what  is  the  time? 

6.  When  3  times  the  yearly  interest  =  -fo  of  the  prin- 
cipal, what  is  the  rate  per  cent? 

7.  When  i-  of  the  interest  for  2  yr.  =  -^  of  the  prin- 
cipal, what  is  the  rate  per  cent? 

8.  When  -|  of  the  interest  for  3  yr.  —  -£$  of  the  prin- 
cipal, what  is  the  rate  per  cent? 

9.  The  interest  for  8  mo.  is  -fa  of  tht>  principal :  what 
is  the  interest  of  $200  for  1  yr.  4  mo.  ? 

10.  If  the  interest  for  1  yr.  4   mo.,  is  ^t-  of  the  prin- 
cipal, what  is  the  interest  of  $100  for  1  yr.  8  mo.  12  da.? 

11.  In    what   time   will  any  principal,  at   5   per   cent, 
give  the  same  interest  as  in  4  yr.,  at  10  per  cent? 

12.  The  interest  of  A's  and  B's    money  for  3J  yr.,  at 
5  per  cent,  is  $40,  and  A's    money  is  twice  that  of  B's : 
what  sum  has  each? 

13.  Twice  A's  money  =  3  times  B's;    and  the  interest, 
at  7  per  cent  for  1J-  yr.,  of  what  they  both  have,  is  $49 : 
how  much  money  has  each? 

14.  One-half  of  A's  money  =  f  of  B's ;  and  the  interest 
of  f  of  A's  and  -J-  of  B's  money,  at  4  per  cent,  for  2  yr. 
3  mo.,  is  $18:  how  much  has  each? 


LESSON  LXXX. 

1.  If  12  peaches  are  worth  84  apples,  and  8  apples  are 
worth    24    plums,  how   many  plums    shall   I   give    for  5 
peaches  ? 

2.  Divide  32   peaches  among  Mary,  James,  and  Lucy, 
giving  Mary  2  more  than  Lucy,  and  Lucy  3  more  than 
James. 

3.  Five  times  a  certain  number  is  16  more  than  3  times 
the  same  number:  what  is  the  number? 

4.  A    has   J   as  much  money  as  B ;    B  has  J-  as  much 
as  C ;    C  has  $15  more  than  A:    how  much  has  each? 

5.  If  f  of  James's  money  be  increased  by  $6,  the  sum 
will  equal  what  Thomas   has;    both    together  have    $34: 
how  much  has  each? 

6.  A  farmer  sold  f  of  his   sheep,  but    soon    afterward 
purchased  -f   as    many  as    he   had   left;    he  then  had  65 
sheep:  how  many  sheep  had  he  at  first? 

7.  If  3   men  can    perform  a  piece  of  work  in  4  days, 
working  10  hours  a  day,  in  how  many  days  can  8  men 
perform  the  same  job,  working  6  hours  a  day? 

8.  Thomas  bought  a  number  of  apples,  at  2  for  3  ct, 
and    as    many   more    at   2  for  5  ct. ;    he   sold   all  at  the 
rate  of  3  for  7  ct. :  how  much  per  dozen  did  he  gain  ? 

9.  A,  B  and  C  rent  a  pasture    for  $92;    A  puts    in    4 
horses  for  2  mo. ;  B,  9  cows  for  3  mo. ;  and  C,  20  sheep 

(134) 


PROBLEMS.  135 

for    5    mo. :    what    should    each   pay,  if  2   horses  eat  as 
much  as  3  cows,  or  as  much  as  10  sheep? 

10.  A    father   who    had    as    many   sons    as    daughters, 
divided   $20    among   them,  giving   to    each  daughter  $2, 
and  to   each  son  $3 :  how  many  children  had  he  ? 

11.  A  gentleman  meeting  some  beggars,  found  that  if 
he    gave   each   of  them  3  ct.  ho  would   have  12  ct.  left, 
but   if  he   gave  each  of  them  5  ct.  he  would   not   have 
money  enough  by  8  ct. :  how  many  beggars  were  there  ? 

SOLUTION.— To  give  each  beggar  5  ct.  took  5 — 3  =  2  ct.  more 
than  to  give  him  3  ct.;  to  give  all  the  beggars  5  ct.  each  took  12  -}-  8 
=  20  ct.  more  than  to  give  them  3  ct.  each;  then,  there  were  as  many 
beggars  as  2  ct.  are  contained  times  in  20  ct.,  which  are  10. 

12.  A  father  wishes  to  distribute  some  peaches  among 
his  children ;    if  he  give  each  of  them  2  peaches  he  will 
have  9  left,  but  if  he   give  each  4  peaches  he  will  have 
3  left:  how  many  children  has  he? 

13.  A  hare    is    10    leaps    before  a  hound,  and    takes  4 
leaps    while    the   hound    takes    3;  but    2  of  the  hound's 
leaps  equal  3  of  the  hare's:    how   many  leaps  must   the 
hound  take  to  catch  the  hare? 

SOLUTION. — One  of  the  hound's  leaps  =  |  of  the  hare's,  and  3  of  them 
—  4£  leaps  of  the  hare;  then,  in  taking  3  leaps,  the  hound  gains  on  the 
hare  4£  —  4  =  £  a  leap.  Since  the  hound  gains  \  a  leap  in  taking  3 
leaps,  he  gains  1  leap  in  taking  2  times  3  =  6  leaps,  and  he  gains  10 
leaps  in  taking  10  times  6  =  60  leaps. 

14.  Henry  is  7  steps  ahead  of  John,  and  takes  6  steps 
while   John   takes   5;  but   4  of  John's   steps  equal  5  of 
Henry's:    how    many  steps    must  John  take  to  overtake 
Henry? 

15.  If  1  ox  is  worth  8  sheep,  and  3  oxen  are  worth  2 
horses,  what  is  the  value  of  1  horse,  if  a  sheep  is  worth 
$5? 


136     KAY'S    NEW   INTELLECTUAL   ARITHMETIC. 

16.  A  and  B  had  24  ct. ;  B  said  to  A,  "Give  mo  2  ct. 
and  I  shall    have   as   much   money  as   you   have  now : " 
how  many  cents  had  each? 

17.  The  age  of  A  is  ^  the  age  of  B ;  twice  the  age  of 
A  is  J  the  age  of  C ;  C  is  20  yr.  older  than  B :  what  is 
the  age  of  each  ? 

18.  If  §  of  A's  money  equals  f  of  B's,  and  f  of  their 
difference  is  $15 :  how  much  money  has  each  ? 

19.  If  10  gal.  of  water  per  hour  run  into  a  vessel  con- 
taining 15  gal,  and  17  gal.   run  out  in  2  hr. :  how  long 
will  the  vessel  be  in  filling? 

20.  Charles   bought    a   number    of  eggs  at  2  ct.  each, 
and   twice   as   many  at  3  ct.  each;    he  sold  them  at  the 
rate  of  3  for  10  ct. :  what  per  cent  did  he  gain  ? 

21.  Mary  wishes    to   divide    some  cherries  among   her 
playmates ;    she    finds   if  she    give    each    of  them    5  she 
will  have  21  left,  but  if  she   give  each    8    she  will  have 
none  left:  what  is  the  number  of  her  playmates? 

22.  Henry  is   30  steps   before   John,  but  John  takes  7 
steps  while  Henry  takes  5 :  supposing  the  length  of  their 
steps   to    be   equal,  how  many  steps   must  John  take   to 
overtake  Henry? 

23.  My  chain    cost   ^    as  much  as  my  watch ;    3  times 
the  price  of  my  chain  and  twice  the  price  of  my  watch 
ure  $100:  what  did  each  cost? 

24.  A  can  do  a   piece    of  work  in  4J  days ;    A  and  B 
together  in  2f  days:  in  what  time  can  B  do  it  alone? 

25.  I  bought  a  number  of  pears  at  2  for  1  ct.,  and  as 
many  more  at  4  for  1  ct. ;  by  selling  5  for  3  ct.  I  gained 
18  ct. :  how  many  pears  did  I  buy? 

26.  A  note  for  $50,  bearing  interest  at  6  per  cent,  and 
due   in    3    years,  was    disposed  of  by  the   holder  for  its 
face,  2   years   before  it  was  due:   what  per  cent  was  the 
discount? 


PllOBLEMS.  137 

27.  A  lady  wished  to  buy  a    certain  number  of  yards 
of  silk    for    a   dress :    if  she   paid   $1  a  yard  she  would 
have  $5  left,  but  if  she  paid  $1J  a  yard,  it   would  take 
all  her  money:  how  many  yards  did  she  want? 

28.  If  $5  be  taken  from  f  of  A's   money,  the  remain- 
der will  equal  B's ;    both  together  have  $51 :    how  much 
has  each? 

29.  If  §   of  the   gain   be    -^  of  the   selling  price,  for 
how  much  will  3f  yards  of  cloth  be  sold,  that  cost  $4  a 
yard? 

30.  A   hare   is    100^  leaps  before  a  hound,  and  takes  5 
leaps  while  the  hound  takes  3 ;   but  3  leaps  of  the  hound 
equal  10  leaps   of  the    hare:    how  many  leaps  must  the 
hound  take  to  catch  the  hare? 

31.  Thomas's   age   is   3  times  that  of  James,  and  the 
difference  of  their  ages  is  10  years:  how  old  is  each? 

32.  John   started   from  C  the  same  time  that  George 
started  from  D  ;  when  they  met,  f  of  the  distance  John 
had  traveled  was  £  of  the  distance  George  had  traveled  ; 
from  0  to  D  is  86  miles  :  how  far  had  each  traveled? 

33.  I  sell  a  certain  kind  of  cloth  for  24  cents  a  yard, 
and  make  20^  ;  if  I  could  buy  it  for  25  per  cent   less, 
and  should  sell  it  at  30  cents  a  yard,  how  much  greater 
would  be  my  profit? 

34.  If  I  sell  a  lot  of  eggs  at  6  ct.  a  dozen,  I  will  lose 
12  ct.,  but  if  I  sell  them  at    10  ct.  a  dozen,  I  will  gain 
18  ct. :  what  did  they  cost  a  dozen? 

35.  The  age  of  A  is  twice  the  age  of  B,  and  f  of  B's 
age -f- 44    years   equals  2^  times  the  age   of  A:   what  is 
the  age  of  each  ? 

36.  Three   towns,  A,    B,    and    C,  are    situated    on    the 
same  road ;  the  distance  from  A  to  B  is  24  miles,  and  •£ 
of  the  distance   from  A  to  B    equals   fy   of  the   distance 
from  B  to  C :  how  far  is  it  from  A  to  C? 


138      KAY'S    NEW    INTELLECTUAL  ARITHMETIC. 

37.  A,  B,  and  C  can  do  a  piece  of  work  in  4  days,  A 
and  B  in  8  days,  B  and  C  in  6  days:  in  what  time  can 
each  do  it  alone? 

38.  A  provision    dealer  bought  a  number  of  ducks,  at 
the  rate  of  6  for  81;  and  twice  as  many  chickens,  at  the 
rate  of  8  for  $1 ;  by  selling  them  at  the  rate  of  2  chickens 
and  1  duck  for  8J,  he   gained    $2J:    how  many  of  each 
did  he  buj'? 

39.  To  buy  a  certain  number  of  oranges,  at  8  ct.  each, 
requires  6  cents  more    than    all   the   money  James   has ; 
but  if  he  buy  the  same  number  of  lemons,  at  3  ct.  each, 
he  will  have  29  ct.  left:  how  much  money  has  he? 

40.  A  rides    10   miles    in    1J-  hours,  and  B,  8  miles  in 
If  hours :   how  far  will  B  travel  while  A  is  traveling  18 
miles  ? 

41.  If  A  had  J  as  many  dollars  more,  and  $2^  besides, 
he  would  have  $40 :  how  many  has  he  ? 

42.  A  person  having  three    sons,  A,  B.  and    C,  willed 
-J  of  his  estate   to  A,  J  to  B,  and  the   remainder   to  C; 
the  difference   of  the   legacies    of  A    and    C   was    $1GO : 
what  amount  did  each  receive? 

43.  A  man  and  his  wife    consume   a   sack   of  meal  in 
15  days ;  after   living  together  6  days,  the  woman  alone 
consumed  the  remainder  in  24  days :   how  long  would  a 
sack  last  either  of  them  alone? 

44.  If  sugar,  worth    3J    cents   a    pound,  be   mixed  in 
equal  quantities  with  sugar  worth  6^  cents  a  pound,  how 
many  pounds  of  the  mixture  will  be  worth  $1  ? 

45.  The  age  of  A  is  5  times  the  age  of  B,  and  the  age 
of  B   is  twice  the   age  of  C.     A  is  45  years  older  than 
C :  what  is  the  age  of  each  ? 

46.  The  age  of  Mary  is  f  of  the  age  of  Ella,  and  the 
sum  of  their  ages  is  6  years  less  than  twice  the  age  of 
Ella :  what  is  the  age  of  each  ? 


PROBLEMS.  139 

47.  A   and   B  together  can  do   a  piece  of  work  in  16 
days ;  they  work  4  days,  when  A  leaves,  and  B  finishes 
the  work  in  36  days  more:  in  how  many  days  can  each 
do  it? 

48.  A  man  bought  84   eggs,  which  he  intended  to  sell 
as  follows:    3  dozen,  at  1  ct.  apiece;    2  dozen,  at  4  eggs 
for  3  ct. ;    and   the  rest  at  4  eggs  for  5  ct. :  but,  having 
mixed    them,  how  must    he  sell   them   per  dozen  to  get 
the  intended  price? 

49.  A   man  agreed  to  pay  a  laborer  $2  for  every  day 
he  worked ;  the  laborer,  for  every  day  he  was  idle,  was 
to  forfeit  $1 ;  at   the   expiration   of  20  days  he  received 
$25 :  how  many  days  was  he  idle  ? 

SOLUTION. — If  the  laborer  had  worked  every  day  he  would  have 
received  20  times  $2  =  $40;  then,  he  lost  by  being  idle  $40  —  $25  = 
$15.  Every  day  he  was  idle  he  lost  $2  -f-  $1  =  $3;  then,  he  was  idle 
as  many  days  as  $3  are  contained  times  in  $15,  which  arc  5. 

50.  James   was   hired    for   30   days;   for   every  day  ho 
worked  he  was  to  receive  30  cents,  and  for  every  day  ho 
was  idle  he  was  to  pay  20  cents  for  his  board ;  at  tho 
end  of  the  time  he  received  $5 :  how  many  days  did  he 
work  ? 

51.  There  are  two  pieces  of  muslin,  each  containing  the 
same  number  of  yards  ;  to   buy  the  first,  at  12^  cents  a 
yard,  requires  40  cents  more  than  to  buy  the  second,  at  10 
cents  a  yard :  how  many  yards  in  each  ? 

52.  Noah  is  35  steps  ahead  of  Moses,  and  takes  7  steps 
while  Moses  takes  5;  but  4  of  Moses's  steps  equal  7  of 
Noah's :  how  many  steps  must  Moses  take  to  overtake 
Noah? 

53.  If  1  man  does  as  much  work  as    2  women,  and  1 
woman  as  much  as  3  boys :  how  many  men  would  it  take 
to  do  in  1  day  what  12  boys  are  a  week  in  doing? 


140      KAY'S    NEW   INTELLECTUAL   ARITHMETIC. 

54.  A  farmer's   sheep   are   in  three  fields;    the  second 
contains  4  times  as  many  as  the  first;  the  third  contains 
3  times   as  many  as  the   second,  and   70  more  than  both 
the  first  and  second :  how  many  sheep  are  there  in  each 
field? 

55.  A  laborer  engaged   to  work  24  days,  for  $2  a  day 
and  his  board ;  he  agreed  to  pay  50   cents  a  day  for  his 
board  when  he  did  not  work ;  at  the   end  of  the  time  he 
received  $38 :  how  many  days  did  he  work  ? 

56.  Three  persons,  A,  B,  and  C,  are  to  share  a  certain 
sum  of  money,  of  which  A's  part  is  $12 ;  this  is  %  of  the 
sum  of  the  shares  of  B  and  C ;  f  of  C's  share  is  equal  to 
T^  of  the  sum  of  the  shares  of  A  and  B :  what  is  the 
share  of  each  ? 

57.  For  how  much  should   a  package  of  sugar  weigh- 
ing 6-J-  Ib.  be  sold,  to  gain  16§  per  cent,  when  sugar  costs 
8  cents  a  pound? 

58.  Two   men    formed    a    partnership    for  1  year;    the 
first  put  in  $100,  and  the  second,  $200:  how  much  must 
the  first   put  in  at  the    end  of   6  months,  to  entitle  him 
to  J  the  profit? 

59.  If  I  sell  my  sugar  at  9  cents   a  pound  I  will  lose 
$1,  but   if  I  sell  it  at  12  cents  a  pound,  I   will  gain  50 
cents:  how  many  pounds  have  I? 

60.  B  is  pursuing  A,  who  is  some  distance  in  advance; 
B  goes  4  steps  while  A  goes  5,  but  3  of  A's  steps  equal 
2   of  B's;    B  goes   36  steps   before    overtaking    A:    how 
many  steps  is  A  in  advance  of  B  ? 

61.  John  bought  5  oranges  and  James  4  oranges;  they 
were  then  joined  by  Thomas,  and  each  one  ate  an  equal 
part  of  the  oranges ;  when  Thomas  left,  he  gave  them  9 
cents :  how  should  this  be  divided  ? 


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ENGLISH  LANGUAGE. 

HARVEY'S  LANGUAGE  COURSE. 

By  THOMAS  W.  HARVEY,  A.  M. 

HARVEY'S  REVISED  ELEMENTARY  GRAMMAR   AND 

COMPOSITION.     I2mo.,  cloth,  160  pp. 
HARVEY'S  REVISED  ENGLISH    GRAMMAR,  I2mo.,   half 

roan,  264  pp. 

A  practical  course  in  Oral  and  Written  Language  Lessons,  Com- 
position and  English  Grammar.  The  Golden  Mean  between  the  too 
labored  attempt  at  simplification,  and  thescientific  technical  gram- 
mar. 

HOLBROOK'S  NORMAL  SERIES. 

By  A.  HOLBROOK,  Principal  National  Normal  University. 

HOLBROOK'S  TRAINING  LESSONS,  121110.,  135  pp. 
HOLBROOK'S  COMPLETE  ENGLISH  GRAMMAR,  I2mo., 
cloth,  204  pp. 

PINNEO'S  GUIDE  TO  COMPOSITION. 

A  Series  of  Practical  Lessons  designed  to  simplify  the  Art  of  Writing  Composition, 
By  T.  S.  PINNED,  A.  M.,  M.  D.  i2mo,  cloth,  162  pp.  Designed  for  those  who  desire 
a  concise  but  comprehensive  course  of  Instruction  in  Composition. 

PINNEO'S  EXERCISES  IN  FALSE  SYNTAX. 

tamo.,  104  pp.  Systematically  arranged  ;  contains,  also,  promiscuous  examples  of 
correct  and  incorrect  syntax. 

PINNEO'S    EXERCISES  IN    PARSING   AND    ANALYSIS. 

i2mo.,  i2o  pp.  A  brief  review  of  the  leading  principles  of  Grammar,  conveniently 
arranged  for  reference ;  followed  by  a  well-arranged  series  of  selections  from  the  best 
authors,  with  explanatory  notes  and  references. 

WILLIAMS'S  PARSER'S  MANUAL 

The  Parser's  Manual,  embracing  classified  examples  in  nearly  every  variety  of 
English  construction.  By  JOHN  WILLIAMS,  A.  M.  i2mo.,  cloth,  264  pp. 

OBJECT  LESSONS  AND  COMPOSITION. 

Things  Taught :  Systematic  Instruction  in  Composition  and  Object  Lessons.  By 
Dr.  M.  E.  LILIENTHAL  and  ROBT.  ALLYN,  M.  A.  Prepared  by  order  of  the  Cin- 
cinnati School  Board.  i6mo.,  96  pp. 

LANGUAGE  EXERCISES. 

For  Primary  Classses.  By  J.  MICKLEBOROUGH,  Prin.  Cincinnati  Normal  School, 
and  C.  C.  LONG,  Prin.  2oth  District  School,  Cincinnati. 

PART  I.     For  First  and  Second  Reader  classes,  121110.,  48  pp. 

Part  II.     For  Third  and  Fourth  Reader  classes,  i2mo.,  96  pp. 

TEACHER'S  EDITION,  12010.,  187  pp.  Contains  Parts  I  and  II  ;  Course  of  Study  in 
Language  Lessons  for  Cincinnati  Schools;  plans  for  developing  the  Exercises  and 
methods  for  presenting  them;  and  much  valuable  information  and  many  suggestive 
hints  for  the  successful  teaching  of  Language. 

These  Exercises  follow  the  Language  Course  lately  adopted  by  the  Cincinnati  Peda- 
gogical Association. 


ECLECTIC  EDUCATIONAL  SERIES. 

NEwEGLECTic  PENMANSHIP, 


/i  simplest,  most  legible,  and  business-like  style  of  Capitals  and  Small 
Letters  is  adopted.  In  the  Copy-Books  each  letter  is  given  separately  at 
first,  and  then  in  combination ;  the  spacing  is  open ;  analysis  simple,  and 
indicated  in  every  letter  when  first  presented ;  explanations  clear,  concise, 
and  complete  are  given  on  the  covers  of  the  books,  and  not  over  and  around 
the  copies. 

NEW  ECLECTIC  COPY-BOOKS.— Revised  and  Re-engraved. 

No's  i,  2,  3,  4,  5  Boys,  5  Girls,  6  Boys,  6  Girls,  6%,  7,  8  Boys,  8  Girls,  and 
No.  9.  Girls'  Copy- Books  identical,  word  for  word,  with  the  Boys',  but 
in  smaller  hand-writing.  First-class  paper,  engraving,  and  ruling. 

ECLECTIC  ELEMENTARY  COURSE. 

The  Elementary  course  comprises  three  books,  smaller  than  the  Copy- 
Books,  but  the  same  in  form.  No's  i  and  2  are  Tracing-Books. 

ECLECTIC  PRIMARY  COPY-BOOK. 

A  complete  Primary  Penmanship,  designed  for  use  during  the  second  year 
of  school  life.  It  contains  all  the  small  letters,  figures  and  capitals,  each 
given  separately  and  of  large  size,  the  object  being  to  teach  the  form  of 
the  letter.  It  is  designed  to  be  written  with  the  lead-pencil.  Furnished 
either  in  white  or  manilla  paper. 

ECLECTIC  EXERCISE-BOOK. 

Contains  a  variety  of  exercises  especially  designed  to  develop  the  differ- 
ent movements,  and  so  arranged  as  to  give  as  much  or  as  little  practice 
on  each  exercise  as  may  be  desired.  It  is  a  little  larger  than  the  Copy- 
Books,  and  has  a  strong  cover,  so  that  the  latter  may  be  placed  within  it, 
thus  making  it  convenient  to  keep  the  two  together. 

THE  ECLECTIC  PRACTICE-BOOK 

Is  made  of  the  same  size  and  weight  of  paper  as  the  Copy-Books,  ruled  with 
double  lines  for  No's  i,  2,  3,  4,  and  with  single  lines  for  the  higher  numbers. 

NEW  HAND-BOOK  OF  ECLECTIC  PENMANSHIP. 

A  Key  to  the  Eclectic  System  of  Penmanship.  A  complete  description 
and  analysis  of  movement  and  of  the  letters,  and  a  brief  summary  of  what 
is  required  in  teaching  penmanship. 

ECLECTIC  WRITING-CARDS. 

72  No's  on  36  Cards.      One  Letter  or  Principle  on  each   Card:    Capital 
Letter  on  one  side,  Small  Letter  on  the  reverse.     Each  illustration  accom- 
panied  with   appropriate    explanations   and   instructions.     Size   of  Cards, 
9x13  inches ;  loop  attached  for  suspending  on  the  walls. 
SAMPLE  BOOK  OF  ECLECTIC  PENMANSHIP. 

Containing  nearly  200  copies  selected  from  all  the  Copy-Books  in  the 
Series.  Will  be  sent  by  mail  for  15  c.  to  any  teacher  or  school  officer  desir- 
ing to  examine  it  with  a  view  to  introducing  the  Eclectic  Penmanship. 

ECLECTIC  PENS.  _-—•—- 

School  Pen,  No.  too,  90  c.  per  gross;  small  box  (2  doz.)i  25  c.  Com- 
mercial Pen,  No.  200,  90  c.  per  gross.  Ladies'  Pen,  No.  300,  90  c. 
per  gross.  Free  Writing  Pen,  No.  400,  90  c.  per  gross.  Sample  Card 
of  Eclectic  Pens,  10  c. 

VAN  ANTWERP,  BRAGG  &  CO.,  Putlisters,  Cincinnati. 


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UNIVERSITY  OF  CALIFORNIA  LIBRARY 


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McGuffey's  Speller, 
McGnffey's  Readers, 
Harvry  s  Speller, 
Harvey's  leaders, 
Ray?c  Arithmetics, 
Ray-     \rpDr^ 


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Morion  s   Physics, 
Brown's  Physiology. 

nrKle's  U,  S.  History, 
71  v         ,iers  Histories, 


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